Citation
The emission of long-range alpha particles in the fission process

Material Information

Title:
The emission of long-range alpha particles in the fission process
Creator:
Bethune, Glen Roberts, 1940-
Publication Date:
Language:
English
Physical Description:
ix, 147 leaves. : illus. ; 28 cm.

Subjects

Subjects / Keywords:
Alpha rays ( lcsh )
Nuclear fission ( lcsh )
Stopping power (Nuclear physics) ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF

Notes

Thesis:
Thesis--University of Florida, 1969.
Bibliography:
Bibliography: leaves 144-146.
General Note:
Manuscript copy.
General Note:
Vita.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
The University of Florida George A. Smathers Libraries respect the intellectual property rights of others and do not claim any copyright interest in this item. This item may be protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work have responsibility for determining copyright status prior to reusing, publishing or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. The Smathers Libraries would like to learn more about this item and invite individuals or organizations to contact the RDS coordinator (ufdissertations@uflib.ufl.edu) with any additional information they can provide.
Resource Identifier:
030405526 ( ALEPH )
16919130 ( OCLC )

Downloads

This item has the following downloads:


Full Text

PAGE 1

THE EMISSION OF LONG-RANGE ALPHA PARTICLES IN THE FISSION PROCESS By GLEN ROBERTS BETHUNE A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1969

PAGE 2

ACKNOWLE D GEMENTS The author is grateful to the ch a irm a n of his supervisory com m ittee, Dr. M. L. Mu g a, for his guidance in the execution of the research and his cooperation in the prep a ration of this dissertation. The consideration of two other committee members, Dr. F. E. Dunn a m and Dr. E. E. Muschlitz, is also appreciated. To the final two committee members, Dr. R. J. Hanrahan and Dr. J. D. Winefordner, the author would like to express his s : Lnce:!'e appreciation and thanks for many years of help within the department. The author is al s o grateful to Mr. W. E. Stee ge r for an excellent job of machining the chamber, to Mr. D. J. Burnsed for his helpful advice and assistance with the electronics, and to Mr. A. C. Cassiato for assistance in handlin g the ch a mber at the reactor. The author is indebted to Mr. Henry Gogun, of the UFTR staff, and his assistants, Mr. Paul Roberts, Mr. Jim Hollis, and Mr. Jim Cooper, for supplyin g copious amounts of neutrons. Thanks also go to Mr. Harvey Norton, of Radiation Control, for assistance in a variety of ways. For assist a nce, endless encoura g ement and concern throu rs hout the years, the author is sincerely g rateful to ii

PAGE 3

Mr. Charle s R. Rice. Finally, the author would lik e to expre s s special thanks to his wife, Sherry, for typin g thi s dissert a tion, and, more importantly, for her faith and understand i n g iii

PAGE 4

TABLE OF CONTENTS ACKNO WLEDGEMENTS ................................... Page ii LIST 01r TABIJES . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . vii Chapter I. INTRODUCTION 1 II. LITERATURE REVIEW OF EXPERIMENTAL WORK ; 4 Probability nf LRA Relative to Binary Fissior1 ..... '1 7 Energy Distribution of Lon g-Range Alpha Part i C 1 e S e 12 Angular Distribution of Long -Range Alpha Particles ................... '" . . . J 5 Energy Distribution of the Fission Fragments in LRA Fission.................. 19 Mass Distributjon of the Fission Fragments in LRA F 1 ission . . . . . . . 22 III. HYPOTH ESES AND MODELS FOR LONG-RANGE ALPHA PISSION . 25 Pre-Scissi.on Hypothesi.s .. .... ..... .. 26 Coiniid ent -with-Scission Hypothesis ....... 30 Post-Scission Hypothesis 35 IV. EXPE RIMENTAL APPARATUS AND PROCEDU RE .. ... ... 39 Apparatus and Associated Electronics .... .. 39 Ex perimen tal Procedure ..... ............ ... 54 Data Reduction 61 :tv

PAGE 5

v. VI. EXPERIMENTAL RESULTS AND DISCUSSION Characteristics of the Alpha Particle Alpha Particle Kinetic Energy Pa ge 66 69 Distributions . . . . . . . 75 Fission Fragm ent Kinetic Energy Distributions . . . . . . . 83 Total Kinetic Energy Distributions ....... 97 Fission Fragment Mass Distributions ...... 106 CONCLUSIONS 118 Appendices A. CALCULATION OF ACCIDENTAL TRIPLE COINCIDENCE COUNT RATE ..................... 123 B. DERIVATION OF FISSION FRAGMENT MASS EQU/ lr~P ION . . . . . . 125 C. COMPUTER PROGRAM FOR ANALYSIS OF LRA FISSION DATA ......... .............. 130 D. DERIVATION FOR ANGULAR DISTRIBUTION CALCULArrIONS . . . . . . . l~O BIBLIOGRAPHY BIOGRAPHICAL SKETCH V 144 147

PAGE 6

LIST OF TABLES Table I. Su mmary of Reported Literature Values for the Probability of LRA to Binary Pa ge Fission . . . . . . . . . 9 II. Co mp o s ition of Uranium Isoto pe .. ... ........ ~6 III. Avera ge Kinetic Energy Values for LRA Fissio11 . . . . . . . . 86 vi

PAGE 7

LIST OJ? FIGURES Fi g ure Page 1. Three energy distribution curves of lon ran ge alpha particles from pile neutron fission of U 2 3 5 13 2. Angul ar distribution of lon g -ran ge alph a particle s fro m U 235 as obt a ined by Titterton (15) .............................. 17 3. Angular distribution of lon g -ran ge alpha particles from spontaneous fis si on of Cf 252 as obtained by Fra e nk e l (25) .. ....... 17 4. Rel at ive mass yields for fission fra g ments from U 235 thermal neu tr on induced bin a ry and LRA fis sion a s obtained by Schmitt et al. (33) . . . . . . . . 23 5. View of th e open fission cha mbe r 41 6. Head-on vie w of the open fi s sion chamber and cover . . . . . . . . ~2 7. Ass~mbled fiss io n chamber with prc arnp lifiers. 43 8 Complete ch amber asse~bly 9. Various motors and gear mechanism used for chamber control......................... 115 10. Scale drawin g of experimental confi g uration used for lon g -ran ge alpha (LRA) fission studies . . . . . . . . . lt8 11. Dual foil changin g mechanism .. ............ .. 49 12. Schematic dia gram of electronic circuitry 52 13. Rack of electronic equipment used in the eX!)erirnent ........ ........... . . 55 Calibra tio n snectrum for Th 228 in equilibrium with its dau g hter products vii 58

PAGE 8

Figure Page 15. Typical fission fragment calibration sp e ctru m . . . . . . . . . 59 16. Kinetic ener g y distribution of alpha particl es emitted from thermal neutron induced fission of U 235 71 17. Angular distribution of lon g -range alpha partj cles for parity=-1 . . . . . 72 18. An g ular distribution of long-range alpha particles for parity=+l ....... .. ... ..... .... 73 19. Alpha particle kinetic energy distribution for e 1 = 55 and e 1 = 40 .... .. .... ........ 79 20. Alpha particle kinetic ener gy distribution for e 1 = 85 and e 1 = 70 ..... ........ ...... 80 21. Alpha particle kinetic ener gy distribution for e 1 = 100 .and e 1 = 115 . . . . 81 22. Alpha particle kinetic ener g y distribution for e 1 = 130 and e 1 = 145 ................. 82 23. Fissj on fra gme nt kinetic energy distri bution for e 1 = 40 .. .. .. .. . .. 89 24. Fission fra gm ent kinetic en e rgy distribut:i_on for e 1 .,, 55 ..... ........ .. ,.,, 90 25. Fission fra gm ent kinetic energy distribution for 0 1 = 70 . . . . 91 26. Fission fra gme nt kinetic energy distribution for 0 1 = 85 .. . .... .... .. .. 92 27. Fission fra gment kinetic ener gy distribution for eL = 100 .................. 93 28. Fissiori fra g ment kinetic energy distribution for e 1 = 115 . . . . 94 29. Fission fragment kinetic ener g y distr ibution for eL == 130 . ... .. .. .. .. 95 30. Fission fragment kinetic energy distribution for e 1 = 145 ................. 96 31. Total kinetic energy ( alpha p ar ticle plus fis si o n fra g mente ) distribution for 0 L = lt O O 9 8

PAGE 9

Figure 32. Total kinetic energy (alph a particle plus fissj_on fra g ments) distribution Page for SL = 550 . . . . . . . . 99 33. Total kinetic ener g y ( a lpha particle plus fission fra g ments) distribution for eL = 70 ~ ................................ 100 34. Total kinetic ener g y (alpha particle plus fission fragments) distribution for e 1 = 85 ................................ 101 35. Total kinetic ener g y (alpha particle plus fission fragments) distribution for e 1 = 100 . . . . . . . 102 36. Total kinetic energy (alpha particle plus fission fra g ments) distribution for eL = 115 . . . . . . . 103 37. Total kinetic ener g y (alpha particle plus fission fra g ments) distribution for eL = 130 . . . . . . . 104 38. Total kinetic ener g y (alpha particle plus fission fra g ments) distribution for 0L = 145 . . . . . . . 105 39. Fragment-mass distribution for Br = 40 110 J.J 40. Fra g ment-mass distribution for BL= 55 ..... 111 41. Fragment-mass distribution for eL 70 . 112 42. Fragment-mass distribution for eL = 85 ..... 113 43. Fragment-mass distribution for BL= ]00 114 44. Fragment-mass distribution for 8L = 115 115 45, Fragment-mass distribution for 0L = 130 116 46. Fra g ment-mass distribution for eL 145 117 47. Vector dia g ram illustratin g conservation of momentum for LRA fission . . . . 127 ix

PAGE 10

CHAPTER I INTRODUCTION As is well known, a nucl e us und e rgoing fission generally splits into two heavy fra gme nts of comparable size. However, the liquid drop model of the nucleus pre dicts, as first pointed out by Present (1), that fi ss ion of a heavy nucleus into three fra gmen ts is dynamically possible. The first observation of the e miss ion of a lon gran g e li g ht particle in the fission process was by Alvarez (2) in 1943. This discov ery was not reported until after the war. Since this first ob ser vation th er e has been a considerable runount of work devoted to the study of these light particles originatin g in the fission process. These subsequent investigations gave stron g evidence tt1at the light particles are mainly alpha particles. Several experimental techniques such as nuclear emulsions, ioni zation cha mb ers, magnetic analysis equip ment, and sernibonductor detectors have been employed in these investi ga tions. The ener gy and angular distribu tions of the alpha particl es a s well as the energy and mass distributions of the associated fission fra gmen ts have been studied. Due to the low probability of e missio n of the long-range alpha particles, the most extensive 1

PAGE 11

2 experim enta l studies have been und er take n only in the past few ye a rs, coincident with the availa b ility of hi gh flux reactors, hi gh current accelerators, multidimensional pulse-hei g ht analy z ers, and semiconductor detectors. These exp erime nts have given a clear indication that the emission process is a complicated one. One of the major reasons for interest in long-ran ge alpha fission (abbreviated as LRA fission) is the use of the alpha p a rticles as a "prooe" of the nuclear configuration at the moment of scission. The detailed exa mi nation of the alpha particle angular and ener gy distributions and the energy and mass distributions of the associated fission fragments in LRA fission gives info rma tion on the shape of the nucleus at scission. The extent of detailed informa tion which c a n be gained from these distributions dep ends of cou rse on the accuracy with which the distributions are determined. The primary pur pos e of this investigation was to determine the various distributions of the alpha particles and the fission fragments in the LRA thermal neutron induced fission of U 235 more exactly than those previously reported and particularly to collect events in which the alpha particles are emitted at small an g les with respect to one of the fission fra gments In the previous inv est gations, the mass distributions of the fission fra gments have be e n calculated only for the cases in which the alpha particles were en1itted in almost a perpendicular direction

PAGE 12

3 to that of the fission fragments. Even in these cases, the equation used for the calculation of the fragment masses is an approximation which ignores the recoil of the alpha particle. In the analysis of the data from this experiment the recoil of the a~pha particle has been taken into account. A solution of the momentum conservation equations for a fragment mass gives a quadratic equation and hence two possible mass combinations are obtained for each fragment. In this work the masses of the fragments are calcu lated regardless of the angle of emission of the alpha particle and the mass distributions of the fragments are found for each angle .. This will be discussed in more detail in a later chapter. In the next chapter a s11rvey on the variety of experiments which have been conducted into the p1 oblem of the emission of a long-range alpha particle in the fission process (LRA fission) will be discussed. The various hypotheses and models which have been proposed to explain the phenomenon will then be presented in Chapter III. Previously, complete surveys on the subject have been made by Perfilov et al. (3) in 1961, Hyde (4) in 1964, Meth asiri (5) in 1965, and by Gindler and Huizenga (6) in 1968.

PAGE 13

CHAPTER II LITE R ATUR E REVIEW OF EXP E RI MEN TAL W ORK Althou g h the emission of lon g -ran ge al p ha particles in the fission proc e ss (abbrevi a t ~ d as LRA fis s ion) w as first observed by Alvarez (2) in 1943, the fir s t published work on the subject was by Tsi e n San-T s i a n g et al. (7) in 1947. At first, the nature of these p a rticles was u n kno w n and they were sim p ly termed lon g -ran ge p articl e s. Alvar e z used a double ionization chamb e r to ob s erv e the particles and Tsien S a n-Tsi a n g et al. used the e m ulsion technique. Vast amounts of data have been collect e d by a wid e variety of exnerirn e nt a l techniques and this topj c i s p resented next under the followin g headin g s: n a ture of the lon g ran g e compon e nt, probability of LRA rel a tive to binary fission, ener g y distribution of lon g -ran g e alph a par t icles, an g ular distribution of lon g -ran ge al p h a par t icle s ener g y distribution of the fission fra g m e nts in LRA fission, and finally, the m a ss distribution of the fission fra g ments in LRA fission. Nature of the Lon g -R a n g e Comnonent Already in the first experiments attem p ts were m a de at es ta bJ ishin g the identity of the lo ng -ran g e particles. From the g rain spacin g alon g the tracks, Wollan et al. (8) 1,

PAGE 14

concluded that the particles were not protons but were most likely alpha particles. Farwell et al. (9) reached 5 the same conclusion from an experiment using double ioni zation chamb e rs. Tsien San-Tsian g et al. (7) perfo rme d calculations on the three-pron ge d forks ob ser ved in the nuclear emulsion in an attempt to estimate the mass of the third particle. The deviation in the angle between the fission fra gme nts from 180 was used to perform the calculation, but the results were not accurate enough to rule out the possibility of such nuclei as He 3 11 6 etc. Allen and Dewan (10) obtained additional evidence in 1950 that the lon g -ran ge particles are alpha particles by a direct m e asurement of the energies of the li g ht particle s from slow neutron fission of U 235 with the utilization of a high pressure double ionization chamb er They also measured the ran ges of the li g ht particles in a separate experiment by using a fission chamber, a proportional counter and aluminum absorbers. A comparison of the ener gy and ran ge distributions showed that the lon g -ran ge particl es were alpha particles. Fulmer and Cohen (11), in 1957, once more and most accurately verified that the particles acco m panying the fission of U 235 were alpha particles. These authors made use of the method of magnetj_c defJ ection to ge ther with a pulse-height analy ze r. The particles were detected with a CsI(Tl) crystal scintillator. Scintillation pulse hei gh t vs Hp (product of ma gne tic field and radius) data sho wed

PAGE 15

6 that the particle had the same value Z 2 /m as alpha particl es The second part of the experiment consi s ted of a deter mination of th e ran ge -ener gy relationship for the particles in aluminum. This proved that the particle s had the same value of mZ 2 as alpha particles. But if the compared par ticles have the same values of Z 2 /m and mZ 2 then they must have the same values for both their char ge and mass. Since the charge and mass of the light particles were the same as the char ge and mass of alpha particles, it was firmly established that the lon g -range particles produced in fission are, in the overwhelmin g majority of cases, alpha particles. The possibility, of course, still existed that a very small percent of the light particl e s could be some other light nuclei. Recently several ex p eriments h a ve been perform e d in an attempt to identify and determine the fre quency of other light nuclei emitted in the fission process. Sowinski et al. (12) measured the relatively intensities of other light particles (H 1 H 2 H 3 and He 6 ) associated with thermal neutron fission of U 235 by using a ~E-E counter tele3cope. They found that there were 2 protons, 0.6 deuerons, 5,5 tritons and 0.8 helium-six nuclei emitted for each 100 alpha particles. Whetstone and Thomas (13) used a simil ar method to identify the light charged par ticles spontaneously emitted from Cf 252 They fou11d that a s ma ll p e rc ent of these li ght particles were due to light nuclei such es H 1 H 2 H 3 He 3 He 6 He 8 He 10 Li and Be.

PAGE 16

7 None of the experiments of this type established that the various light char ge d particl es other than He 4 observed from fissionin g systems were actually emitted in coinci dence with fission. Recently Raisbeck and Thomas (48) became the first to observe these various light particles in coincidence witl1 fission fragments. They were able to investigate the angular distributions of these particles relative to the fission axis as well as the kinetic ener g y spectra. However, the percentage of these particles is small an~ throughout the remainder of this discussion, only alpha particles will be consid ere d as the light particles emitted in the fission process. Probability of LRA Relative to Bin a ry Fission Long-range alpha particles are emitted in the fission process with a frequency of approximately 1 in 400 binary fissions. Many investigators hav e measured the relative probability of double and triple fission with various methods of nuclear physics hein g u sed Thermal neutron induced fission of U 235 has been studied in the greatest detail, but neutron induced fission of U 233 (10,111), Pu 239 (10,14), and Pu 241 (14) as well as spontaneous fission of Cf 252 (13, 14, 26, 47), Pu 240 (14), Pu 242 Cm 242 (14), and Cm 244 (14) hav e all been studied. The data of various authors are not in good a g reement, due, apparently, to the low statistical accuracy of the measure ~ c n ts and the poor detection efficiency of the method

PAGE 17

8 employed. In the thermal neutron induced fission of U 235 the values reported are in the range 1:250 to 1:550. The various results for different nuclides are shown in Table I. The various methods used to determine the probability of LRA to binary fission include emulsions (15,16,17), ion ization chambers (9,14), proportional counters (10), a magnetic spectrograph (11), semiconductor detectors (18) and a semiconductor ~E-E counter telescope (13). The reported probabilities for LRA fission for the cases in which fission is induc e d by fast neutrons or char g ed particles are in conflict. Tsien San-Tiang et al. (7) indicated that fission of uranium and thorium with the emission of long-ran g e alpha is not observed with fast neutrons. The authors concluded that this type of fission is characteristic only of the lower excited st at e s of the nuclei undergoing fission. However, it was late1 found (19) that fast neutrons can induce LRA fission. Perfilov and Solov'eva (20) measured the probabilities of LRA to binary fission for fast neutron induced fission to be 1:600 and 1:1100 for 2.5 MeV and 14 MeV neutron energies respectively. V. A. Hattangadi et al. (21) found only a small decrease in the probability of LRA to binary fission when the energy of the neutrons inducing fission was changed from thermal to 3 MeV neutrons. Schroder (18) found the LRA to binary fission ratio to be essentially c o rn t an t forincid e nt n e utron ener g ies betwe e n 0. 003 eV

PAGE 18

Nuclide ~T 2 3 5 V u23s u23s u23s u23s p2~5 V 0 23s u23s U23S t;235 TABLE I SUMMARY OF REPORTED LITERATURE VALUES FOR THE PROBABILITY OF LRA TO BINARY FISSION Investigator Farwell et al.(9) Green and Livesey(l6) Marshall(l7) Allen and Dewan(l0) Titterton(l5) Fulmer and Cohen(ll) Nobles(l4) Schroder(18) Perfilov and Solov'eva(20) Hattangadi et al.(21) Source Slow neutrons from cyclotron Slow neutrons Thermal neutrons Thermal neutrons Slow neutrons Pile Neutrons Thermal neutrons Thermal neutrons 2.5 MeV neutrons 14 MeV neutrons Thermal neutrons 3 MeV neutrons Method Ionization chamber gold absorbers Photographic plates Emulsions Proportional counter Emulsions Magnetic spectrograph aluminum absorber Ionization chambers Solid state detectors Emulsions Emulsions Solid state detectors Solid state detectors Frequency 1:250 1:340 30 1:230 1:550 50 1:422 50 1:310 1:499 30 1:490 20 1:600 1:1100 1:650 10 1:780 10

PAGE 19

Table I continued Nuc l ide Investigator Source Method Frequency u233 Allen and Dewan(lO) Thermal ::1eutrons Proportional counter 1:405 30 u~33 Nobles(l4) Thermal neutrons Ionization chambers 1: 414 20 Pu239 Allen and Dewan(lO) Thermal neutrons Proportional counter l: l t 45 35 Pu2:ig Nobles(l4) Thermal neutrons Ionization chambers 1:411 26 1 MeV neu t rons Ionization chambers l"f'252 Whetstone and Spontaneous tiE-E counter 1:309 .1. Thomas(l3) fission cr2s2 Nobles(l4) Spontaneous Ionization chambers 1:299 18 fission ,...f'252 Muga, Bowman and Spontaneous Nuclear emulsions 1: Lll5 41 V.l Thompson(47) fission cr2s2 Watson(26) Spontaneous Scintillator1:345 20 fission proportional counter

PAGE 20

11 and 0.3 eV. Lovel a nd et al. (22) induced fission in thin targets of Th'32 U 235 U 238 and Np 237 by bombardm e nt with protons, deuterons) and helium ions of various energies up to 42 MeV. They found that the LRA to binary fission ratio falls somewhat as the energy varies from zero (spon taneous fission) to approximately 6 MeV (slow neutron fis sion) and then it changes more slowly, if at all, as the energy is further increased. Nobles (14) plotted the relative probability of LRA fission against Z 2 /A of various nuclides. The data indi cated a trend of increasing probability of emission of long-ran g e particles with increasing Z 2 /A values and decreasin g probabjlity with increasing excitation energy in a given nuclide. Loveland et al. (22) found the follow ing empirical relation to be valid for their data. If= 0.13 (X 43) x 103 (2.1) In this equation, X = 3.2Z A. The dependence of the LRA to binary fission ratio on either Z 2 /A or Equation 2.1 cannot be explained by any known theory. There seems to be a dependence of the ratio on the target nuclide, excitation energy and probably on the angular mornentum of the fissioning nucl e us. The dis crepancies whjch exist in the reported data make it impos sible to determine exactly the form or extent of this dep e nd e nce.

PAGE 21

12 Ener gy Distribution of Lon g -R a n g e Al ph a P a rticles The ener g y distribution of long-ran g e alpha particles extends fro m an experiment a l cut off point of about 6 MeV to 30 MeV with a broad peak around 15-17 MeV and a full width at half-m a xi m~ m (FWH M ) of about 10-12 MeV. The energy spectrum has been studied by emulsion s (7,15,16,23), by absorption in thin aluminum foils (10), by a CsI crystal scintill a tion apparatus (14), by ionization chambers with a grid (10), by a high resolution ma g netic spectro g raph (11), and by solid state detectors (24,25,26). The results reported by the various authors on several different iso topes are impressively constant. Titterton (15), Allen and Dewan (10), and Fulmer and Cohen (11) all found the peak of the ener g y spect r u m to be at 15 MeV for either pile or thermal neutron induced fission of U 235 These three distributions are sho w n in Figure 1. The energy spectra of lon g -ran g e alpha particles from spontaneous fis sion of Cf 252 and thermal neutron induced fission of U 235 were found to have maxima at 17 1 MeV and end-point energies of 29 1 MeV. Watson (26) found the long-ran g e alpha peak for Cf 252 to be at 16 M e V, while Fraenkcl and Thompson (24) ieasured the spectrum at an angle of approx imately 90 with respect to the fission fra g ments and found it peaked at 14 MeV. When the alpha particle spectrum was measured without re g ard to its an g le with the direction of the fission fra gme nts, the most p r obable en e r g y w a s 15 M eV.

PAGE 22

I= = c::, LL.I > Ic:r:: _..., L1.J 0::: 800 700 600 500 400 300 200 100 0 4 B I cl I 8 I I I I I I I I I I I I I I I I I I 12 1 ENERGY ( M eY) I 20 I 24 13 ::L, 28 Fig. 1.-Three energy distribution curves of long-ran g e alpha particles from pile neutron fis s ion of U 235 (Graph reproduc e d fro m Fulm er and Cohen (11). Distributions A, B, and C were deter m ined by Fulmer and Cohen ( 11), Allen and Dev rn n ( 10), and by Titterton (15), r e spectively.)

PAGE 23

Hattangadi ~t ~l. (21) investigated the spectrum of long-range alpha particles in 3 MeV neutron induced fission of U 235 They found the spectrum to be very similar to the one for pile neutron induced fission. The peak for 3 MeV neutron induced fission was 1 or 2 MeV higher and the FWHM was about 2 MeV less than the correspondinG values in pile neutron fission. Perfilov et al. (27) did not, however, find any appreciable change in width in 14 MeV neutron induced fission of U 238 compared with that in the thermal neutron fission of U 235 In spontaneous fission of Pu 238 and Pu 2 .. 0 Perfilov et~! ( 28) observed the peak of the spectrum at about 17,3 and 17.0 MeV respectively and the spectrum of alpha particles from all plutonium nuclides seems to be shifted towards larger energies but have smaller FWHM values compared to those of the alpha spectrum from uranium nuclides. The most accurate determination of the energy spectrum of long-range alpha particles produced in the thermal neutron induced fission of U 235 was done by means of a magnetic spectrograph by Fulmer and Cohen (11), whose work has been mentioned previously. The hi g h resolving power of the apparatus made it possible to obtain high precision data. The results of these measurements revealed that the energy distribution was continuous and without fine structure.

PAGE 24

15 An g ular Distribution of Long-R a n g e Alpha Particles The angular distribution of long-range alpha particles in the fission process is strongly peaked at about 80-85 with respect to the light fission frag me nts. For many years the use of nuclear emulsions (7,15,29) was the only method used in the investigation of this angular distri bution. This method is both simple and reliable but suffers from low counting statistics. The developm e nt of solid state detectors has provided another method for determining the angular distribution. Titterton (15), using emulsions, investigat e d the angular distribution for slow neutron induced fission of U 235 He found the p e ak near 85. This distribution is shown in Figure 2. It can be seen from this figure that there is a significant number of ev e nts for which the deviation fro m the mo s t probable value is large. Titterton concluded from the shape of this graph that the alpha par ticle could not be emitted from one of the moving fission fragments but that the distribution supported the view that the alpha particles, in most cases, were left at rest be tween and acquire their energy by repulsion fro m the fis sion fragments. According to Perfilov and Solov'eva (29), the angular distribution of the alpha particles becom e s broader with increasin g ran g e of the alpha, and for alpha particles with ranges great e r than 200 (E > 21 M e V) it approaches an isotropic distrlbution. Further, th e an g le of emission of

PAGE 25

the alpha particles was found to be indep ende nt of the asymmetry in the r anges (therefore, independent of the ener gy and mass) of the fission frag me nts. 16 The properties of the alpha particles emitted in the spontaneou s fission of Cf 252 have been ex ami ned in a three param e ter correlation experiment usin g semiconductor detec tors by Fraenkel and Thompson (24). The angular distribu tion (see Fi g ure 3) of the alpha particles was found to be peaked at an angle of 81 with respect to the direction of the light fra gment It is approximately symmetric with respect to this angle and has a FWH M of 32.5. Their angular distribution is more symmetric and has a narrower width than the one obtained by Titterton (15). Fraenkel and Thompson had a hi g h accidental coincidence r ate at the smaller and lar ge r angles with respect to the li ght fi ssi on fragments and this gives a constant back g round to the angular distribution and is especially important for the outer wings (s ma ll and large angles) of the distribution. Fraenkel (25) corrected the angular distribution for th e finite size of the detectors and the source (s ee Figure 3). It follows, because of the approximations used in the correction procedure, that the correct shape of the dis tributions is so mew hat in doubt. This is particula~ly true for the outer wings of the distributions, w here the series expansion u s ed in the correction procedure does not conver ge r apid ly. For the se two r easo ns, there is some doubt as to th e correctness of the outer wings of this distribution.

PAGE 26

::z: 17 I -17-1 56 _, >= 48 UJ I:z: 0 40 Ln = LLJ a.. 32 v., ::.c:: 24 = ILL c:, 16 = UJ = == 8 = :z: 0 0 30 60 90 150 ANGLE (DEGREES) Fi g 2.-A ngu lar di stributi on of lon g-range aJ p ha particles from U 2 35 as o b tain ed by Titterton (lS) 2 X 10 4 --.--,-1 & 1.5x10 1.-........JL----'L I L __ 60 70 80 90 100 110 120 {9l Fi g 3.-An gu lar distribution of lon g -r ange alpha particles fro m soontaneous fission of bf 252 as o btain~d by Fraenkel (25)

PAGE 27

18 These authors also plotted the an g ular distribution of the alpha particles for seven intervals of the fission fra g m e nt energy ratjo RR. They found a shift in the most probable direction of the alpha particle towards the direction of the heavy fra gme nt as the energy ratio RE increased. Thus the peak position of the angular distribution shifted from eL = 72 (the angle between the alpha particle and the light fission fragment) for almost symmetric fission (1.0 ~RE< 1.1) to eL = 99 for very asymmetric fission (RE~ 2.0). This is in conflict with the results of Perfilov and Solov'eva (29) which were mentioned previously. However, Perfilov and Solov'eva had only a small number of events as co n1par ed to Fraenkel and Thompson. The experimental data on the anguJar distributioi1 of alpha particles indicate that the alpha particle is emitted in a region between the two fission fragments. Fraenkel and Thompson explained the systematic shift of the most probable angle with energy ratio (which is, as an approx imation, the same as the mass ratio) on the basis that the most probable point of emission of the alpha particle is strongly dependent on the n1ass ratio. Th e y concluded that this point is close to the heavy fragment for almost sym metric fission and close to the light fra gme nt for very asymmetric fission. This interesting interpretation will be discussed in more detail i11 Chapter III.

PAGE 28

Energy Distribution of the Ji'ission Fragments in LRA Fission 19 In the study of LRA fission by emulsions, it was noted (7,15,17) that in a majority of the events the fis sion fragments have different ranges. The ratio of these ranges was determined to be 1.3, but emulsions are not suitable for a precise measurement of the energy dis tribution of the fragments. Because of this limitation, comparatively little has been known until recently on the energy and mass distribution of the fission fragments in the LRA fission process. Allen and Dewan (10) were the first to measure the kinetic energy spectrum of the associated fragments in the LRA fission of U 235 The usual two peaks were observed indicating asymmetric division of rr.ass, but each peak was shifted to a lower energy than is observed in binary fission. Their spectrum was distorted because the measurements were affected by the angular correlation between the fragments and the alpha particle. The result of this distortion was that the low energy "heavy hump" was considerably higher than the light one and had a larger area. Despite this difficulty, they determined that the peaks of the spectrum are sl1ifted to lower energies by about 10 MeV and 7 MeV for the light and heavy fragments respectively. It was al so observed that the total kinetic energy carried away in LRA fission is about equal to that liberated in binary fission. Dn1itriev et al. (30) found

PAGE 29

20 that the peaks are shifted toward lower energy by about 9 MeV and 6 MeV for the light and heavy fragments respec tively and that the half widths (FWHM) of the spectrum peaks are less than those for the binary fission spectrum. From these investigations it seems that the sum of kinetic energies of the most probable fragments in binary fission is approximately the same as the sum of kinetic energies of the most probable fragments and of the alpha particles in LRA fission. Therefore the equation (2.2) can be written where is the most probable total kinetic energy of the two fragn1ents in binary fission, is the most probable total kinetic energy of the two fission fragments in LRA fission and is the most probable a energy of the long-range alpha particle. Solov'eva and Filov (31) confirmed this result and concluded that this equation remains valid for all portions of the alpha par ticle spectrum. However, Dmitriev et al. (32) found that the shifts in the peaks from the binary fjssion values of light and heavy fragments kinetic energies vary with the energy of the emitted alpha particles. For alpha particle energies greater than 15 MeV, they found the shifts in the heavy and light peaks to remain constant; thus Equation 2.2 can be applied only for the alpha particles in the region below 15 MeV. Schmitt et ~l. (33) found the total frag 1n ent kinetic

PAGE 30

energy averaged over all mass ratios and over all alpha particle energies in the LRA fission of U 235 to be 21 155 2 MeV. Adding to this a most probable alpha particle energy of 15 MeV, we obtain a value of 170 MeV as the average total kinetic energy of the fragments and alpha particles released in thermal neutron induced LRA fission of U 235 For spo11taneous fission of Cf 252 Fraenkel and Thompson (24) measured the average total kinetic energy in LRA fission to be 185.2 0.1 MeV, compared to 181.1 0.1 MeV released in binary fission. The average total kinetic energy of the fission fragments only in LRA fission was 169.0 0.1 MeV. For their energy spectrum (25), the high energy fragment peak in LRA fission is shifted by approximately 7 MeV compared to binary fission, whereas the low energy peak is shifted by only t1.5 MeV. The results of the investigations of the energy spectrum in the LRA fission process have given generally similar results. Thereforej it can be concluded that the average total kinetic energy released in LRA fission (including the alpha particle energy) is about the same, or no more than 3 to 4 MeV higher than the average kinetic energy released in binary fission. The average total kinetic energy of the fission fragments (excl11ding the alpha particle energy) in LRA fission is about 12-13 MeV less than in binary fission. Halpern (34) concluded from this reduction of the fragment kinetic energy in LRA fis sion that the configuration of the fragments at scission

PAGE 31

22 is more elongated in LRA fission than in binary fission. He estimated the distance between the fra g ments at scission in LRA fission to be 13 percent greater thin the distance in binary fission. Mass Dist~ibutiort bf the Fission Fragments in LRA Fission Schmitt et al. (33) determined the masses of the fission fragments in LRA fission for U 235 For the calcu lation of the masses, the simple momentum and mass conser vation relations were used: M 1 E 1 = M 2 E 2 and M 1 + M 2 = 235 + 1 4. The first equation is the same one used in binary fission. Therefore, recoil from the alpha particle and from prompt nentron emission is neglected. They found that the peaks in the mass distribution for LRA fission are shifted towards low mass values compared with those in binary fission. This is shown in Figure 4. The important feature of this comparison is that the low mass side of each peak is identical, within statistical uncertainties, for binary and LRA fission. The high mass sides of the peaks in LRA fission are displaced downward with respect to the high mass sides of the peaks in binary fission. It was concluded from this that the alpha particle is emitted principally at the expense of nucleons in the light fragment for near-symmetric fission and at the expense of nucleons in the heavy fragment for more asymmetric fis sion. Furthermore, the mass distribution w a s obtained for four energy intervals of the alpha particle spectrum and

PAGE 32

7 6 5 4 = _, LL.J >Li., >Ic::: _, LW 3 0:: 2 0 2 3 e 0 Q coee I 70 Fi g I I ( 80 90 100 110 120 1 3 0 1 4 0 150 160 7 0 FRAG M E N T MA SS (A MU) 4.R elative mass yiel d s f or fissio n f ragments fr om U 2 35 th ermal n eutr o n i ndu c ed b i n a ry a nd LRA f is sion as o btained by Schmit t et a l. ( 33 )

PAGE 33

24 it was observed that the distribution of the fission fragment masses is essentially independent of lon g -range alpha particle energy. For high energy alpha particles the peak to valley ratio app e ars to be reduced and this has been interpreted (5) to indicate that coincidence with high energy alph a particles shows a higher symmetric yield than that in coincidence with low energy alpha particles. The main features of the experimental data on LRA fission have been discussed. The problem now turns to a theory or model which wjll explain the mechanism respon sible for this complex process. Various authors have advanced several hypotheses. These will be discussed in the next chapter.

PAGE 34

CHAPTER III HYPOTHESES AND MODELS FOR LONG-RANGE ALPHA FISSION Although the emission of long-range alpha particles in fission was discovered about twenty-five years ago, its mechanism has never been satisfactorily explained. Large amounts of experimental data have been obtained, but as noted in the previous chapter, the results are often in conflict. Even for the cases in which there are no dis crepancies in the data, any interpr e tation of the results in terms of a mechanis m for LRA fission is, in general, not unique. As would therefore be expected, many hypoth~ eses, models and mechanisms have been proposed to explain LRA fission. The various proposals can be broken into three hypotheses which are concerned with the time at which the alpha particle is emitted. Within each of these hypotheses, there are several models and mechanis~s which have been presented in an attempt to explain the LRA fission process in more detail. The three hypotheses which contain the various models and mechanisms are the pre-scission hypothesis, the coincident-with-scission h y pothesis and the post-scission hypothesis. 25

PAGE 35

26 Pre-ScTs s j_on Hypoth es is Allen and Dewan (10) were the fir s t to propose that the alpha particle could b e emitted before the instant of scission. They reasoned that the alpha particle could be emitted fro m the neck of the compound nucleus where the magnitude of the potential barrier is reduced. Thus the process can be visualized as a special type of alpha decay. If fission occurred immediately after alpha particle emission, the alpha particle would then be accelerated in the Coulomb field of the other two fragments. This would explain the energy and angular distributions of the alpha particles. This mechanism seems also to qualitatively account for the decrease in the probability of lon g -ran g e alpha emission in fission with increasing excitation energy, since the lon ge r the lifetime of the compound nucleus, the more probable should be the emission of alpha particles. More recently, Ramanna et al. (35) proposed that alpha particle emission in fission is the result of evap oration of these particles from the excited and deformed compound nucleus having a large an g ular mom e ntum and with a charge polarization along the fra g ment axis. The emis sion of alpha particles takes place at the neck of the distorted nucleus where the barrier is de p ressed so that they come off preferentially in a plane per p endicular to the line of fli g ht of the fra gm ent s Th e purpo s e of th e charge polarization is that it serves to reduce the barrier at the neck for all types of distortion. The an g ular

PAGE 36

27 mom e ntum of the compound nucleus was incorporated into this model because it was observed experimentally (35) that the alpha particles have a forward-backward peakin g with respect to the incid e nt neutron direction for fast neutron fission and this is a characteristic of evaporation from a compound nucleus having a large angular momentum. The decrease in probability of LRA fission with increase of incident neutron ener g y can be accounted for in that alpha particle and pre-scission neutron emission are competing modes and depend on the excitation energy of the compound nucleus. Neutron emission is more favorable at higher excitation energy than alpha particle emission. At the same time, the probability of alpha particle emission should decrease with increasin g excitation energy since alpha particles are emitted from the neck re g ion and tl1e likelihood of alpha particle cluste~s being there decreases as the excitation ener g y increases. The pre-scission or evaporation hypothesis can account for many experimental results of the LRA fission process. It can qualitatively account for the energy and angular distributions of the alpha particles, the decrease in probability of LRA fission with increasin g excitation energy, and the forward-backward peaking of the alpha particles in fast neutron induced fission. The main objections to this hypothesis are that (1) it is unable to explairi the an g ular correlations of the alpha particles with mass ratio of the fission fragment s (2) based on

PAGE 37

28 reasonable values of bindin g en e r g y, pot e nti a l barriers, etc., there is not enou g h en e rgy for this m e ch a nism to occur and (3) the tim e involved for evaporation is much longer than one expects in th e fission process. The an g ular correlations of the alpha particles with mass ratio of the fragm e nts were discussed in the previous chapter. The pre-scission or eva p oration hypoth esis predicts that the most probable an g le of the alpha particles, with respect to the light fission fra g ment, should decrease as the mass ratio of the fra g ments incr e ases. This is not found to be true. Perfilov and Solov'eva (29) observed the angle of emission of the alpha particles to be independent of the asymmetry of the fission fra g ments, while Fraenkel and Thompson (24) found that the most prob able an g le of the aloha particles shifted tow a rd the he a vy fra g ment as the energy ratio (which is approximately equal to the mass ratio) incre a sed. The second objection was analyzed by Fulmer and Cohen (11). They ar g ued that if the alpha particles are evaporated, their energy distribution is determined by two factors: the temperature distribution inside the nucleus (Maxwellian) and the penetrability of the Coulomb barrier. It tt1rns out that the tail of the experimental energy distribution of the alph a particles a g rees well with the tail of a Maxwellian distribution correspondin g to a tem p erature of 1.11 MeV. Therefore th e nen e trability of th e Coulo m b ba r rier for particles w i th en e r gy in exc e ss

PAGE 38

of 17 MeV is equal to unity. They made use of this and con structed th e depend e nce of barrier p en etrability on 29 th e energy of the alpha particles in the low energy region. They concluded that an effective charge of about 20 must be ascrib e d to the nucleus emitting the alpha particle. It could be argued that the lar ge barrier penetrability mi ght be caused by a lowering of the Coulomb barrier near the neck of the compound nucleus. However, it was estim ated (3) that for this to happen an improbably l arge nucl e ar deform a tion would be necessary, since the Coulomb barrier in the neck is a slo w ly decreasin g function of the distanc e betwe en the two fr gments that are bein g formed. Halpern (34) c alcu l ated the relative evaporation rate of alpha particles co mpared w ith that for ne11trons in ord er to show that the alpha particle was not evap orated. He esti ma ted that it cost about 25 MeV to release an alpha pa rticle and about 5 MeV to release a neutron in fissjon. If both particles are produced by evaporation, the ratio of the number of neutrons to alpha particies produced would be about exp [(25-5)/ T] where Tis the nuclear temperature in Me V. From observed neutron spectra, Tw as estimated to be about 1 MeV at scission. On this ba sj s, about 109 alpha particles are expected in fission per neutron. About 103 are obse rved Halpern concludes, therefore, that the obs erved alpha particle yield is much too lar g e to be accounted for by evaporation.

PAGE 39

30 C6indid e nt-With~Scission Hypoth e sis There have been several models proposed in which the alpha particle is emitted at the mom e nt of scission. The purpose of these various models has usually been to explain the energy and angular distribution s of the alpha particle. It was Present (1) who extended the liquid drop model to predict that the division of a liquid drop into three fragments of comparable masses is dynamically possible. As was shown by Present, for lar g e deformations correspondin g to fourth harmonics, two necks can be formed which become breaking points as the drop is elongated. Tsj en San-Tsiang et al. (7) modified this model to allow the central drop to be a light particle. They reasoned that the excitation energy of the nucleus due to the capture of a neutron is transformed into deformation energy of the compound nucleus. The deformed nucleus forms a dumbbell shape in which the neck of this nucleus will become the light particle. All three of these frag ments touch each other up to the instant of scission. At scission they break apart under the influence of Coulomb forces. The velocity and dir e ction of motion of the light particle depend on its initial position relative to the other two fragments. Its motion will be in the direction of the resultant of the Coulomb forces of the heavy fragments. This model explains the observed angular distribution of the alpha particles and makes possible an estimat e of the most probable energy of the alpha

PAGE 40

31 particle which is in good agreement with the valu e obtain ed from experiments. Such a description of the mechanism of LRA fission is but qualitative. This model does not explain why, in the majority of cases, alpha particles are produced in place o~ other light nuclei. Furth e r, this model cannot explai1i the observed probability for LRA fission and its dependence on neutron energy, as well as the connection betw ee n the an gu lar and energy correlations of the alpha particles and the fission fra gme nt s Halpern (34) has proposed a model for the emission of long-rang e alpha particles based on the id ea that scission is an extremely violent and non-adiabatic process. This model describes the phenomena of LRA fission as a sudden approximation or snappin g process. Halpern has calculated the energy required to re mo ve an alpha particle from one of the fragments and place it in the re g ion between them. This value is a b out 25 MeV. The excita tion energy of the fragments at scission is not sufficient to account for the energy of the emitted alpha particle. But durin g the fission process, the distortion ener gy of the stretched nucl e us is converted to deformation ener gy of the fra gmen ts just after scis s ion and due to the sudden sucking in motion of the neck of the deformed fra gme nt, an alpha particle may be left behind in the region between the two fra gm~nts In discussin g the application of the sudden app roximation to fis s ion and the mechanism of how the alpha pa r ticl e is emitted, it is necessa ry to u se a

PAGE 41

32 wave mechanic a l rather than a classic a l formulation since the particle wavelengths are of the sa me ord e r as the syste m dimension s In the sudden approximation the wave function remains unchan ged This corresponds to the cla ss ical statements that the po s ition and momentum re mai n the sam e It is assumed that the potential chan ges asso ciated with scission are instantaneous. The alph a particle wave function do e s not chan ge durin g the instant of scission, but after scission the part inside nuclear matter is quickly absorbed leavin g only the part ori g inally in the neck of the fissionin g n u cl e us. The surviving p a rt of the wave function represent s a free alpha particle in the region between the fra gme nts. After th e alpha particle is left between the fra gw ent s it i s then acc e lera te d by the Coulo m b force of the two char ge d fra gm2 nts. The proba bility of LRA fission depend s on the fissionin g nucleus, fra gme nt mass division, fra gme nt kinetic ener gy distortion energy and excitation energy of the fissionin g nucleus. The larger the distortion of the two fra gm ents just after scission the larger the probability of the expected alpha particle emission. For example, when the total distortion in both fra gme nts is very small th ere may not be enou g h en e r gy present for the ejection of an alpha particle. For fr agme nts with lar ge distortions, the snap back is more ener g etic and there is more chance to eject an alpha p ar ticle. This sudden appro ximati on or sna pp in g process model gives a good explanation for the reduction

PAGE 42

33 of the fra gment kinetic energy in LRA fission. From this reduction in frag ment kinetic ener gy H alpern calculated the distance between the fra gm ents at scission to be 13 percent la rger in LRA fis s ion tl1an in nor mal bin ary fission. It is clear, from the sudden snap model, that only in long elongations of the distorted compound nucleus has enough energy been stored to make alpha particle emission possible. The decreased fra gme nt kinetic energy and the increased separation distance of the fragments at scission can therefore be understood from this model. Assuming that the alpha particles start at the scission point in the Coulomb potential, Halpern (36) computed the energy and angular distribution of alpha particles. From these calculations and from exp2rimental data, he concluded that by the time the ~ucleus actually tears in fission, the future fra~ments have already acquired considerable kinetic energy. In those events where the neck between fragments lasts lon ge st, the frag ment kinetic energy at scission is largest, althou gh the final kinetic energy for these events is smallest. In these scissions, the energy stored in distortion is lar ge r than average. It is mainly in these lon g -neck events that the fission alpha particles are produc e d. They are left behind between the fra gm ents at scission, acquiring the needed energy for escape from the nuclear matter throu g h the agency of non-adiabatic potential chan g es. These changes arise fro m the snap-back of the fra gmen t walls

PAGE 43

34 toward equilibrium shap e s just after scission. Not all of the LRA fission data can be quantitatively understood in terms of this picture, but none of the data are in signif cant conflict with it. Fraenkel and Thompson (24) and Fraenkel (25) advanced a model in which the scission point varied its position along the neck of the distorted nucleus in response to the mass ratio of the fission fragments. They concluded that the point from which the alpha particle is emitted is close to the heavy fragment for almost symmetric fission and close to the light fragment for large mass ratios. Their resul~s indicated that it should be assumed that the alpha particles are emitted at the scission point or within a distance of the order of 1 fermi from this point and very close to the moment of scission, before the two fragments are widely separated (within 1021 seconds from the moment of scission). They then arrived at the conclusion that the scission point is close to the heavy fragment for almost symmetric fission and it shifts towards the light fragment as the mass ratio increases. Probably the most important conclusion of these authors was th~t the LRA fission process is very similar in all its aspects (except for the alpha particle emission) to the binary fission process. The most striking evidence for this conc~usion was the great si1nilarjty of the fission fragment energy ratio distribution for the two processes, and the similarity of the sin g le fra g ment ener g y distribu

PAGE 44

35 tions as a function of the energy ratio. The primary purpose of the model of Fraenkel and ri'ho m pson was to explain the shift in the most probable direction of the alpha particle towards the direction of the heavy fragment as the energy ratio of the fission fragments increased. These experimental results are satisfactorily explained by this model. This model of interpretation of Fraenkel and Thompson is actually based upon the 11 geometrical 11 model of mass division in binary fission from Whetstone (37). The model of Fraenkel and Thompson does not actually describe the mechanism by which the alpha particle is emitted nor does it explain why usually an alpha particle, rather than some other light partjcle such as a neutron, proton, triton, etc., is left behind in the fission process. Post-Scission Hyoothesis Feather (40), in 1947, first su g gested that the alpha particle emitted in LRA fission could be evaporated from one of the fission fragments after scission had occurred. The conditions required were that the evap oration be from a highly excited fragment produced in a binary division and that it lie in a particular range of nuclei which are unstable, or almost unstable, against alpha emission in the ground state. More recently, Feather (38,39) has examined the experimental evidence of Apalin ~-t al. (Lil) on the number of secondary neutrons in LRA f1sslon, and of Sch m itt. ~-t a 1:_. (33) on the kinetic energies and masses of the fra g ments

PAGE 45

36 in LRA fission. From these results, several conclusions were drawn. The alpha particles must be emitted from a system which, in relat1on to energy, is relatively "cold" (excitation energy not more than a few MeV). In this connection, the experiments of Apalin et al. (41) and Schmitt et al. (33) show that the initial excitation energy of the fragments is reduced, on the average, by about 6 MeV as a result of alpha particle emission. Feather (38,39) reasoned that if the alpha particle in LRA fission is emitted almost immediately after scission from a newly formed fragment, it is necessary, first of all,to determine what would be the energy available for alpha disintegration if the fragment were undeformed but possessed the energy of excitation characteristic of the fragment at the moment of its formation. Feather made a series of calculations and decided that the hypothesis of alpha particle emission from a newly formed fragment was a credible one if applied to the heavy fragments (Af > 130) in U 236 fission, but very much less credible if applied to the light fragments. Moreover, in relation to the heavy fra gm ents, the hypothesis was more easily credible for those fragments of small neutron excess than for the fragments of large neutron excess, over the whole range of Af involved. Another requirement for the hypothesis to be acceptable is that the alph~ particle must escape from the region of the deformed fra gmen t within some 1015 seconds of the instant of scission. This requirement is

PAGE 46

37 effectively the requirement of almo st in sta ntaneous esc a pe. Feather arrived at the final conclusion that the hypothesis having the strongest claim to attention is that which assumes that the alpha particl es ori gi nate in the heavy fragments exclusively, bein g liberated very shortly after the instant of scission, with a probability not much less than unity, from fragment nuclei of low yield and small neutron excess. This is the two-sta ge hypothesis or model. In order to explain the observed angular distribution of alpha particles fro m this model, it is necessary to suppose th a t the alpha particles are emitted opposite to the direction of motion of the parent fra gme nt. This means that the alpha particle must be emitted b etwee n the fra gme nts probably from the tip of the collapsin g pro tuberance, which is that portion of the neck of the compound nucleus belon gi n g to the heavy fra g ment immediately after scission has taken place. But Halpern (34) has argued that if the alpha particles are evaporated from fission fra gme nts, they would tend to be emitted from the outer ends of the fragments rather than into the central region where the Coulomb barrier is much thicker. This two-stage model should also predict,that as the mass ratio of t}1e fra gme nts becomes lar ger the most probable angle of the alpha particle should become smaller with resp e ct to th2 15 g ht fission fra gment The results of Fra e nkel and Tho mps on (24) are in dir ec t conflict to this prediction.

PAGE 47

Nardi and Fraenkel (42) have recently investigated the LRA fission neutron s of Cf 252 and determined the variation of neutron yield with fragm en t mass in binary and LRA fission. There was a great similarity between the curves. It is generally assumed that the excitation ener g y of a fragment in low ener gy fission results from the defor mation ener gy of the fragments immediately followin g scission. This similarity in the neutron yield with fra ment mass for LRA and binary fission indicates that the behavior of the deformation ener gy of the fission fragments is very nearly the same for both binary and LRA fission. If the alpha particles were always emitted from the heavy fragment, this would not be true and the neutron yield with fra gment mass for LRA fissio n would not re semb le so closely the curve of binary fission for the heavy fragment region. Nor would the curve for LRA fission be expected to be lower than that of binary fission for th e li g ht fragment re g ion. These results make it seem very unlikely that the alpha particles are emitted in a two-sta ge process and predominantly, or exclusively, from the heavy fragments. No real progress towards a solution for a th e ory or mechanism of LRA fission has been made in the past fe w years. There have been numerous hypotheses and models advanced and each of these can explain some aspects of the experimental results, but none c an explain all of the results and none can give a true picture of the process.

PAGE 48

CHAP'l'EH IV EXPERIMENTAL APPARATUS AND PROCEDURE The properties of the long-range alpha particles emitted in the thermal neutron induced fission of U 235 were examined in a three-parameter correlation experiment. The procedure involves the detection and parallel energy measurement of the alpha particle and the two fission fragments from a ternary ~vent. Three solid state detec tors were placed at selected angles and at a fixed distance in a plane about a fission source. Signals from the~e detectors were routed to a three-coincident-parameter analyzer having 256x256x256-channel resolution. Apparatus and Associated Electroni~s The experimental apparatus consists of three solid state semiconductor detectors mounted about a source of U 235 F deposited on a thin VYNS film and enclosed in an It aluminum fission chamber. This chamber is 3i inches in diameter a nd 6i inches in length. A view of the open chamber is shown in Figure 5, a head-on view in Figure 6, and a view of the assembled chamber with preamplifiers is. shown in Figure?. The complete chamber assembly which consists of fission chamber, preamplifiers, exhaust tube, cables, motors, and gear mechanism js about 6 feet in 39

PAGE 49

~o length and is shown in Figure 8. A view of the various motors and gear mechanism used for control of the cha mber is shown in Figure 9, A uranium source was mounted (see Figure 5) in the center of the chamb e r. The uranium sources were prepared by slowly evaporating, in vacuum, U 235 F 4 onto 10-20 ~ g /cm 2 VYNS film supported on thin (0.015 cm) stainless steel washers. The U 235 F 4 deposit was confined to a circular area 0.238 cm in diameter by a collimation system. Sources ran gi ng from 0.10 to 0,37 mg/cm 2 (1.0-3,7 x 104 g/cm 2 ) thickness were fabricated and used in the expe riment. The thickness was determined by alpha p a rticle countin g with a solid state detector system of known geometry. The source was mounted so that a normal to the uranium side of the foil (see Figure 10) would bisect the angle between fission fra gme nt detector X and alpha particle detector Y. The uranium isotope was obtained from the Oak Ridge National Laboratories and had the composition indicated j n Table II. The two fission fra gment detectors (X and Z) were of the surfacebarrier type fabricated from 300 n-cm n-type silicon with a sensitive area of 0.25 cm 2 (5mm x 5mm). Normally, these two detectors were operated at 30 volts back-bias and were usually replaced before the current exceeded 8 microamps. The 2lpha particle detector (Y) was also of the surface-barrief type and was fabricated f rom 8,000 n-cm n -type s 1 licon. Its sensitive area w as the sa m e s:lze (5mm x 5mm) as thRt of the f jssio n fra gme nt

PAGE 50

6 INCHES GRAPHIC S CALE CHAMBER COVER EXHAUST TUBE DRIVE ROD FOR FOIL CHANGING MECHANISM Fig. 5.-View of the open fission chamber FOIL CHANGING MECHANISM FISSION FRAGMENT DETECTOR X

PAGE 51

0 .5 O 3 INCHE S l!!!!!!!liiiiif!!!!liiiiiiiii!!!!!!!!!!!!!!!!!!!!!!!!!iiiiiiiiiiiiiiiiill!!!!!!!!!!!!!!!!!!~ GRAPHIC SC ALE FISSION CHAMBER BASE FOIL CHANGING MECHANISM DETECTOR ARM 90 FOIL POSITION CHANGER CHAMBER COVER Fig. 6.-Head-on view of the open fission chamber and cover

PAGE 52

43 Fig. 7.-Assembled fission chamber with preamplifiers

PAGE 53

0. 5 FE E T G R A P H IC SCAL E ,___ S ERVOMOTORS FOR CONTROLLING DETECTOR ANGLES FOIL POSITION MOTOR PREAMPS GEAR MECHANI SM FISSION CHAMBER Fig. 8.-Complete chamber assembly

PAGE 54

Fig. 9.-Various motors and gear mechanism used for chamber control

PAGE 55

detectors. This detector was normally operated with a back-bias voltage of 75 volts giving a depletion depth of greater than 1100 microns, which is sufficient to stop 30 MeV alpha particles. In order to maintain a constant depletion depth for each detector during the course of an irradiation, periodic adjustments (in increments of 1 volt) of the back-bias voltage were made as the current increased. All of the detectors used in this experiment were locally manufactured by the investigator. TABLE II COMPOSITION OF URANIUM ISOTOPE Mass Number 234 235 236 238 Percent 0.038 99,909 none detectable 0.053 The three solid state detectors were positioned around the uranium source in the aluminum chamber. The height of each detector and its distance from the source were adjustable (s9e Figure 5), This allowed the three detectors and the U 235 Fsource to all be placed in the same plane. The Y detector (for alpha particles) was fixed in position while the X and Z detectors (for fission fr a~me nts) were movable. The an g ular position of these

PAGE 56

'-17 two detectors could be varied by reinote control while the chamber was in the reactor. This was accomplished by the detector arms, onto which the detectors were mounted by mean s of a transistor socket, bein g connected to the gear mechanism and servomotors at the rear of the chamber asse m bly via concentric shafts. The angular position of the detectors was reproducible to within 0,5 degree. The radial position of the X and Y detectors was fixed at 2.0 cm from the U 235 F~ source and each subtended a planar angle of l'-1 de g rees or a solid an g le of 0.063 sr (s e e Figure 10). The Z fission fra g ment detector was kept at a distance of 1.3 cm and was used to "shadow" all events observed by the X fission fra g ment detector. It subtended a planar an g le of 22 or a solid angle of 0.1118 sr. A dual foil chan g ing mechanism (see Figure 11), which held a nickel foil on one rod and a natural alpha source on another, was attached to the arm which held the Y detector. This dual foil changing mechanism, by remote control, allowed the following to be placed in front of the alpha particle detector: (a) the nickel foil, (b) the natural alpha source, (c) both nickel foil and alpha source, (d) neither nickel foil nor alpha source. The nickel foil, whose thickness was 7,91 mg/c~ 2 (composed of a 5,65 mg/cm 2 foil and a 2.26 mg/cm 2 foil), prevented fission fragments from strikin g the detector ~hile permittin g alpha particles to 1 ea ch the detector w ith only a sli g ht reduction in

PAGE 57

48 Fig. 10.-Scale dra wi n g of experimental confi guration u sed for long-ran ge alpha ( LRA ) fission studies

PAGE 58

---Ni Foil ---Th 228 Alpha Source Th 228 Alpha Source __ ___,, Ni Foil ---------" Fig. 11.-Dual foil changing mechanism

PAGE 59

50 energy. This essentially prevented accidental triple coincident events and also reduced the amount of radiation damage done to the alpha particle detector. For a calcu lation of the accidental triple coincident rate, see Appendix A. Most of the radiation damage experienced by the Y detector was due to neutrons and gamma rays from the reactor while most of the dama ge experienced by X and Z detectors was due to fission fragments. The count rate for fission fragment detector X was usually 700-800 c/sec while the count rate for detector Z was about 2,000 c/sec. The rate for X and Zin coincidence was usually 75-80 percent of the count rate for X which proves that for binary events, Z did not shadow all events observed by the X fission fra gme nt detector. This was becau se the angle between fission fragment detector X and Z via detector Y was 185 degrees in place of 180 degrees (see Figure 10). This arrangement was necessary because of alpha particle recoil on the flight path of the fission fra gments from LRA fission. This recoil usually causes the an g le bet ween the fragments via the alpha particle to be about 185 de g rees. Of course, this deviation from 180 de g rees depends on the energy and angle of the alpha particle, but is u s ually about 5 degrees. Therefore, it was assumed that each time a fission fragment from a LRA event was d ete cted by X, its complementary fra gmen t was d ete cted by Z.

PAGE 60

51 A schem a tic dia gram of the electronic circuitry is shown in Figure 12. The output fro m each of the three solid state detecto rs was first amplified by preamplifiers placed direc t ly behind th e ch am b er and was then pa ra lleled to two a m plifier systems, one of which (linear or slow amplifier) conserved linear response of the detector pulse; the other (fa st amplifier) pre ser ve s a fast rise time. The latter pulse, after being amplified by a factor of about on e hundred by the fast amplifier, was directed through a 0-7 nsec delay box to a fast discrimin a tor pulse regenerator which was adjusted to deliver a fast rise time pulse of about 30-40 n s ec width. The X and Z discrim inators were set so that pulses from fra gm ents of ener g y less than about 10 MeV could not tri gger the discriminato r to produce an output pulse. This hel pe d to eli1ninate any spurious events which could be caused by line-volt age nois e The Y discriminator was adjusted sufficientl y above the baseline noise so that pulses from particles of ener gy l ess than 4-4.5 MeV could not trigger the discrimin a tor. This discriminator setting, along with the nickel absorb er foil which was placed in front of the Y detector, meant that alpha particles of energy less than about 7.5 MeV (before passing through the nickel foil) could not be det ect ed. The purpose of the discriminator being set at this level was to eliminate background effect from the baseline noise of th e fast pulse. This bas e li ne nois e was c a used by interact i on of n e 11trons and gamm a rays wjth both the

PAGE 61

CPA X CHAMB E R W I TH C P A DETEC TORS y C PA C PA = C H A RG E S E NS! T l V C P REAM P M P A = MU LT I PA R A METER A NALVZ E R F A ST D EL AV FOPR A MP BOX AUTOMATIC LIN E AR GA I N AMP CONTRO L F AST OE LA f F OP R F A ST AM P B OX C O IN C AUTOMA T IC LINEAR G AI N AMP CONTR O L F AS T 0 El A Y F OP R AMP BOX AUTOMATIC LINEAR GAIN AMP CONTROL F OP R = F AST D I SCRIMINAT O R P ULSE REG ENE RATO R Fig 1 2.S c h e m a t ic diag ra m of e l e c t ron i c c i rc u itr y PA PE R TAP"E R E ADOUT GATE t MP A \Jl I'\)

PAGE 62

53 preamplifier and with the 8,000 n-cm alpha p a rticle detector. Interactions with the X and Z 300 n cm fission fragment detectors were much less noticeable. The output pulses from the three fast discriminator pulse regenerators were applied to a three-fold fast coincidence circuit. The triple coincidence output served to open the ADC gates, allowing the outputs of the three linear amplifiers to pass through for subsequent analysis by the analyzer. The analyzer which was used in this experiment is actually a six-parameter analyzer, but only three of the parameters were used and, therefore," it will subsequently be referred to as a three-parameter analyz~r. The triple coincide~ce output pulse would hold the ADC gates open for about 4 microseconds (~sec). The inputs to the ADC's were from Oto -3 volt pulses of approximately 2 sec in duration. When the ADC gates were opened and the three pulses from the linear amplifiers passed through, one pulse was immediately analyzed; the other two pulses were te:mporarily stored and were then released on command and analyzed. This analyzer would measure and store 3 parameters in a maximum time of 245 sec. Upon compl e tion of this three-stage digital conversion, automatic readout on punched paper tape could be achieved or the events could be stored in the memory of the analyzer until a maximum of 255 events had been accumulated and then punched on paper tape. Readout could be caused by manual s e lection at any time.

PAGE 63

Automatic gain control stabiliz e rs were incorporat e d into the linear amplifier systems of the X and Z fission fragment circuits. This system operat e d in the follo w ing way. An integrator circuit counted all pulses within the region above a certain baseline level and below a certain window level. The output of the integration circuit was fed back into a variable-gain amplifier placed between the preamplifier and linear amplifier of that system. The variable-gain amplifier adjusted the forward gain so as to yield a constant count rate within the region of interest and therefore a constant integrator output. The high energy peak (light mass peak) of the binary fission fragment spectrum was chosen for reference, since this point is the most sensitive one for such a system. The purpose of this automatic gain control was to prevent a decrease in gain of the fission fragment pulses as the solid state detectors be g in to deteriorate from radiation damage. A picture of the rack of electronic equipment used in this experiment is shown in Figure 13. Experiment~l Procedur~ The system was completely checked the day previous to a scheduled run at the reactor. The detectors and electronics were checked by using a thick-backed Cm 2 ~~ alpha source or a Cf 2 ~ 2 source which produced alpha particles and fission fragments. The time alignment of the fast pulses was checked periodically with a precision fast

PAGE 64

55 :YI ~ -J I I r ~ i ,_ c=J c:=:l C: ::l /) 3 t : l ti 0 ,,,. Fig. 13.-Rack of electronic equipment used in experiment

PAGE 65

pulser. Adjustment in the time alignment could be made with the 0-7 nsec delay boxes of the system. After the entire system was checked, the detectors, source and foil changing mechanism were enclosed in the aluminum chamber. The cha m ber was then evacuated and a back--bias voltage of about 10 volts was placed on the detectors overnight. On the day of a scheduled reactor run, the evacuated chamber was placed in the thermal column of the University of Florida Training Reactor (UFTR). The thermal column has six 4 inch by 4 inch removable graphite stringers. The upper center stringer was removed to make space available for the chamber. A 4 inch cubic paraffin block and a 4x4x5 inch block of Bi 209 were placed into the stringer column in front of the chamber. The paraffi11 block served to increase the thermal to epicadmium neutron ratio and the purpose of the bismuth block was to shield the detectors from reactor gamma rays while not noticeably reducing the t}1ermal neutron flux. After the chamber was placed in the thermal column, shielding was required to prevent gamma rays and neutrons from streaming out into the reactor cell. The reactor was then taken up to a power of 150 watts for a preliminary checkout and a calibration of the alpha particle (Y) detector. The vacuum of the fission chamber was always less than 10 microns during the experiment. The Y detector calibration was accomplished

PAGE 66

by positioning the natural alpha source in front of the detector. This alpha source was Th 228 in equilibrium 57 with its daughter products and gave a six peak spectrum (see Figure 14). The two alpha particle peaks at 8.78 MeV (Po 212 ) and 6.77 MeV (Po 216 ) were used as the calibration points for the alpha particle detector. The spectrum of Figure 14 was taken with the chamber outside of the reactor. At a power of 150 watts, the peaks were not as distinct but all could easily be seen. The calibration was done at 150 watts because, at a higher power such as 3 kilowatts, the spectrum was some w hat obscured by the interaction of gamma rays and net1 t rons with the 8,000 n-cm alpha particle detector. However, the peak position s did not shift with a chan g e in the reactor power. Upon co m pletion of the procedure at 150 watts, the reactor power was taken to 3 kilowatts. All of the LRA fission data were collected at this power level. The thermal neutron flux intercepted by the chamber at this power was approximately 6 x 10 9 n/cm 2 sec and the thermal to epicadmium neutron ratio at this irradiation site was approximately 30:1. The two fission fragment detectors (X and Z) were calibrated using the two peaks of the single fragment energy distribution in binary fission of U 235 A typical fission fragment calibration spectrum is shown in Figure 15. The energy values for the two peaks were taken from ti ~ e-of-flight ~easuremcnts (43,44). Usually, calibrations

PAGE 67

4500 4000 3500 I 3000 Th228 5.42 Mev Ra224 5.68 Mev Rn220 626 Me, I I i= 2500 J 1 1 Bi212 1,J 6.04 Mev ; 2000 l I 1 1500 7 \ I coo I Po 1 6.77 Mev p 0 212 8. 78 Mev 500 1 I I 0 ~--~u ~~::::::O=O=Q=O::~~ 10 15 20 25 30 CHANNEL NUMBER 35 40 45 Fig. lll.-Calibration spectrum for Th 228 in equilibrium with its daughter products 50 1..,, co

PAGE 68

-' i LLI = ~-== = c.,;, = .u 0.. ..J "" 3 I= = = c.,;, LL. = = = 0 25 r \ \ V 50 75 100 125 150 175 200 CHANNEL NU M BER Fig 15 .Typical fis s ion fra g ment calibration spectrum 225 250 V1 \0

PAGE 69

60 of the detecto rs was done only at the be gi nning and end of an experiment. When the experimental runs at the reactor were longer than the standard 8 hour day, anoth e r calibration was p er for me d about halfway through the experim ent Typically, no gain shift of the reference peak was obser v ed during an experiment for the fission fragment detectors. The energy peak of the heavy fr ag ment usually shifted upwa r d some t w o or three channel numbers (approxi ma tely 1 MeV) during an experim e nt. The coincidence resolving time used in the experi ment was 2T = 60 nsec. This was dete rmi ned experimentally by incorporating a pulser and three 0-128 nsec delay boxes into the system. The resolving tim e determined that, for two fission f ragme nts and an alpha particle to be declared as orig inat in g from the same ev e nt, all three fast pulses were required to arrive within a time interval of 60 nsec. This caused accidental events to be very rare (see Appendix A). At an angle of 85 de gree s (the angle b e tw e en fission fra gme nt detector X and alpha par ticle detector Y), the triple-coincidence rate was approxi ma tely 35-40 counts/hour while the calculated accidental rate was about 1 count every 4 hours. The triple-coincidence rate was reduced conside ra bly at smaller angles until it reached a rate of approximately 1.0-1.7 counts/hour at an angl~ of 40 de gree s. The total exp er i me ntal time (for all an g les) on t r ip l ecoincidence du ring which LRA data we re collec ted

PAGE 70

61 amounted to 201.5 hours. The number of "acceptable" LRA fission events collected in this time totaled 1584. Only about 5 hours on triple-coincid e nce could be obtained for an average day's run. The remainder of the time was used for putting the chamber in the reactor, checkout procedure, calibrations, etc. Data were collected for the following four experi mental angles (0) with respect to the X fission fragment detector: 40, 55, 70, 85. For each experimental angle e, data were collected with respect to both the light and heavy fission fra g ment. Therefore; the four experimental angles actually became eight an g les when the data were reduced so that the angle was always between the alpha particle and the light fission fra g ment (e 1 ). As an example, if the experimental angle was 40 and the heavy fra g ment was detect e d by X, then eL would equal (185 40) or 145. The energy and angular distributions were therefore obtained for the following angles (eL) with respect to the light fission fragment: 40, 55, 70, 85, 100, 115, 130, 145. Since the X detector subtended a planar angle of 14 and the experimental angles were 15 apart, any overlap of an an g ular region was prevented. Data Reduction The data resulting from this LRA fission experiment were transferred to cards for data reduction usin g the

PAGE 71

Univ ersity of Florida IBM 360 computer and facilities. In the reduction process, events for which the alpha particle registered less than 5 ch annel numbers were discarded. The Y discriminator h ad been adjusted to exclude events fro m this region and the occu rrence of any was probably due to lin e-voltage noise. 62 As stated in the previous section, a Th 228 source in equilibrium with its daughter products was used for calibration of the alpha particle detector. The two alph a particle peaks at 8,78 MeV (Po 212 ) and 6,77 MeV (Po 216 ) were used as reference points for a straight-line calibr ation (SLC). This lin ear extrapolation allowed the energy of the alpha particle from each of the LRA fission events to be calculated. A correction was then made for th e energy loss of the alpha particles in the 7,91 mg/cm 2 nick el foil by u sing the range-e11ergy curves of Williamson and Boujot (45). Interpolation of these tables of Williamson and Boujot for energy steps of 0.1 MeV was accomplished by a Taylor series expansion. The corrected alpha particle energy was rounded off to the nearest 0.5 MeV. It was decided not to use LRA fission events with alpha particle energy below 8.0 MeV in the analysis. This cutoff point was cho sen to insure that events due to line-volta ge noise and to baseline detector noise were always eliminated from the data. Therefore, any event whic h had an alpha particle energy of l ess than 8.0 MeV was discarded by the computer.

PAGE 72

63 In the beginning, a straight line calibration (SLC) was applied to the binary fission fra gme nt spectra (obt ained during the calibration procedure of the experiment) by comp arison with that from time-of-flight data (43,44). Approxi mate masses, based on the en e rgies from the SLC approach, were then calculated by means of a auadratic formula. The necessity of using a quadratic formula to calculate the masses of the fission fra gme nt from LRA fission was cau sed by the alpha particl~ recoil on the fra gments The experimental input information used for the solution of the fragment masses consists of three pulse hei g hts (Ex, E 2 Ea), the experimental angle (0), the mass of the alpha particle ( Ma ), and the mass of the fissionin g nucleu s (MX + M 2 +Ma= 236). This limitation on input information actually impo ses tl1e quadratic solu tion. If another angle were accurately known, this quadratic solution would not be necessary. The derivation of this fragment mass relation is given in Appendix B. Two possible masses evolve for each fission fragment since a quadratic for m ula gives two solutions; one mass when the positive sign is u sed in the formula and another mass for the negative sign usage. This sign will be referred to as parity with a negative parity meaning that the ne gative sign was used in the quadratic equation. The negative and positive parity cases were treated sepa rately and a set of resuJ ts and distributions was obtained for each case. For the remainder of this calibration

PAGE 73

discussion, it will be assumed that only one case is being considered and only one mass obtained for each fission fra g ment. 64 The mass-dependent calibration (MDC) described by Schmitt et al. (46) was applied after obtaining the approximate masses based on the SLC approach. A new energy value was obtain e d for each fragment by this method and a new set of masses was then computed. This iteration process was continued until the energy values converged to within 0.5 MeV. These values from the final iteration were then taken as the masses and energies of the fission fra g ments for that particular parity calcu lation. Needless to say, for the complew e ntary parity calculation of the fra g ment mass) another energy value will also be obtained since the MDC causes the fragm e nt energy to be dependent on the fragment mass. Therefore, there are two possible masses and two possible energies for each fission fragment as a result of the quadratic mass equation and the mass~dependent energy caJ ibration. This influence of the"" term of the quadratic equation on the mass and energy of the fission fragments becomes more apparent at extreme angJ.es. That is, the difference between the masses and energies of the fragments calculated for parity=-1 and for parity=+l increases with an increase in the deviation of eL from 90 degrees. After the calculation of the energies and masses of the fragm e nts, the events were divided into two groups:

PAGE 74

65 one group was co m posed of events for which the an g le between the alpha p ar ticle and the light fission fragment (BL) was equal to th e experimental an g le (0) while the other group was compos e d of the events for which BL was equal to 185 B. For each of the BL an g les, the various distributions were tot a led, average energies calculated, etc. The computer program that perform e d this data reduction scheme is given in Appendix C.

PAGE 75

CHAPTER V EXPERI M EN T AL RESULTS AND DISCUSSION As was p r eviou s ly di s cussed, th e detectors were arran g ed in th e fission ch a mbe r such that all events observed by the X fission fra g ment detector would be "shadowed" by fis s ion fra g ment detector Z. This means that only the an g le betwe e n alpha particle detector Y and fission fr a g m ent detector Xis accu ra t e ly kn ow n for a given event, and that angle is known to about degr e es. A solution of the momentum conservation equations (s e e Appendix B) for the t w o fission fr agm ent masses g ives a quadratic equation and, therefore, two possible solutions or mass sets for each fission fra g ment pair. It cannot be kno w n, without exact kno w ledge of two an g les, which calculated result is correct for any giv e n ob se rvation. Each calculation is probably correct in about half of the cases. For an g les close to 90, the"" correction term of the quad r ati~ equation is small and the difference between a fragment mass calculated for parity = -1 and the same fra g m e nt mass calculated for parity = +l is only 1-2 mass units. As has been previously ex p lain e d, parity r ef 2 r s to th e 11 11 si g n which is us e d in the qu a dratic 66

PAGE 76

67 fission fra gme nt mass equation. For pa ri ty = -1, th e neg a tive sign is used in th e quadr a tic equation for the calcul a tion of the fragment mass. The term parity =+ l indicates that the positive si g n is used in the equ a tion. The term parity used her e is not related to the qu a ntu m mechanical parity term which is often used in nuclear physics. At an angle of exactly 90, th e correction term is zero and the equation is no lon g er quadratic. At ext r eme an g les, the correction term becomes larger and the diff e rence in parity=-1 and p a rity =+ l mass valu e s becomes approximately 10 18 mass units for BL= 40 and BL= 145. This difference, of course, depends on the energies of the two fission f ragments and the alpha p a ticle ener gy For BL values less than 90, parity =1 gives the lo w er mass value for the li g ht fr agme nt, which does not vary greatly from the avera g e li g ht frag me nt mass for binary fission. When parity=+l, a lar ge r mass value for the light fr agme nt is obtained and the fra gme nt-m ass distribution beco me s more nearly sy mm etric. For BL greater than 90, the lower mass value for th e light fission fragment is given for parity ~ +l and these distributions sho w two mass peaks similar to the frag me nt-m a ss distributio n observed for bin ar y fission. When parity =1, a lar ger mass value is obtained f o r th e light fission fr a g ment a n~ once a ga in, the fra gme n t-mass distributj on b e c ome s more symmetric.

PAGE 77

68 The fission fra gme nt kinetic energy and total kinetic energy distributions are affected in two ways by a change in parity. First, there is a slight change in the kinetic energy of the fragment when parity is changed. This is due to the change in fragment mass with parity change and the employment of this mass to calculate the kinetic energy of the fragment by the mass-dependent calibration (MDC). This shift in energy is usually less than 1.5 MeV even for a fission fragment mass change of 15 amu. The second way in which the fission fragment and total kinetic energy distributions are affected is by a change in the number of events for a particular angle 8L = 8. If the mass numbers of two fission fragments from a LRA fission event are within a few mass units of each other, then a change in parity (this term refers to the two possible solutions of the quadratic equation of Appendix B) may cause the light fission fragment to become the heavy fragment and vice versa. The value of eL would change from BL= 8 to eL = 185 8 (the comole mentary angle of 8 is taken as 185 8 due to the alpha particle recoil on the path of the fission fragments) and this would remove one event from the individual fission fragment kinetic energy and total kinetic energy distributions at eL = e, and add one event to the distributions at eL = 185 e. The same holds true for the alpha particle kinetic energy distributions. However, the kin e tic ener g y of an alpha particle is independent of the parity value

PAGE 78

69 since the alpha particle has a constant mass and its energy is calculated (s e e Data Reduction Section of Chapter IV) by means of a straight-line calibration (SLC). For each of the various distributions at every angle for which data were obtained, graphs will be presented for both parity=-1 and parity =+ l. This will be done, for consistency and ease of comparison, even for the cases in which the distributions are identical. The experimental results will now be discussed und e r the following topics: characteristics of the alpha particles, alpha particle kinetic energy distributions, fission fragment kinetic energy distributions, total kinetic energy distributions> and fission fra gmen t mass distribu tions. Characteristics of the Alpha Particles A general uncorrelated type alpha particle energy distribution was obtained by collecting a spectrum of the alpha particles from fission in coincidence with only one of the fission fra gme nts. The fission fragment detector was placed at 90 with respect to the alpha particle detector and at a distance less than 1.0 cm from the U 235 foil. At this proximity the detector subtended a planar angle of approximately 30 and, therefore, the alpha particle is essentially uncorrelated with the direction of the fission fragment. This distribution is shown in Figure 16. The error bars represent statistical errors

PAGE 79

70 only. The main characteristics of this energy distribution are the broad peak or maximum around 16 MeV, a full width at half-maximum (FWHM) of 9.5 MeV and an end-point energy of 29 MeV. These values are in good agreement with pre viously reported values (see Figure 1), with the spectrum being almost identical to that reported by Titterton (1 5 ). The primary purpose in collecting this distribution was for comparison with other reported spectra (10,11,15,2 5,47 ) in order to demonstrate that the alpha particle calibration procedure gave reliable results. As can be seen, this purpose was accomplished. In Figures 17 and 18, the angular distribution of the alpha particles as a function of the angle eL between the alpha particle and the direction of the li g ht fra gmen t is presented. Figure 17 is for parity=-1 and Fifure 18 for parity=+l. They are alm~st identical and differ only slightly at the extreme angles. The ordinate on these t wo curves refers to the number of counts per unit solid angle (steradian) rather than geometrical angle. The counts were corrected for the fission fra g ment count rate, for the data collectjor1 time on triple coincidence at each an g le, for the geometrical efficiency of the alpha particle detector about the fission source, and for the solid angle subtended by the detector (se e Aopendix D). The number of counts at 85 was set equal to 1000 and all oth er values were calculated relative to this v a lu e The angular distribution is approximately symmetric

PAGE 80

71 19 0 180 170 160 150 140 130 120 110 (,,) I:z:: LJ..J >100 LJ..J LL.. = = 90 LJ co ::;:;: = 80 z 70 60 50 40 30 20 10 0 0 .,. I .-I I l I I I r T.--.1-rr-.,~--~ 6 8 10 12 14 16 18 20 22 2 4 26 28 ENERCY OF ALPHA (MeV) Fig. 16.-Ki netic energy di stribution of alph a particl e s e mitted fro m th er m al neutron induc e d fission of u23s

PAGE 81

'/ 2 100 0 LLl 900 -' = = c,: = 800 -' = V) ..... 700 = = = Lt..J 600 0.... V) ..... = = 500 = C-'> u.. = = 400 Lt..J 00 ::,;;: = = 300 Lt..J ==..... c,: --' 200 LLl = 100 ~-~--..-----.----.---,---.---, --_.--:;=-=-=-=::;O=:;::::::;::=O~..., 40 50 60 70 80 90 (") 100 110 120 130 140 150 e l Fi g 17.-An gular di st ribution of long-range alpha particle s for parity ~ -1

PAGE 82

73 1000 u.J 900 _, = = ex: = 800 _, = "" t700 = = = u.J 600 0.. "" t= = 500 = CJ LL.. = = 400 LI.J = ::;,; = = 3 00 u.J >tex: 200 _, u.J = 100 ---r--...-----.----.---.--~---r----,.----r--,------r----, 40 50 60 70 80 90 100 110 120 130 140 150 e l Fi g 18.-An g ular distribution of lon g -r ange alpha particle s for parity=+ l

PAGE 83

74 around a most probabl e value of about 83 and it has a FWHM of a r ound 20. The position of the pe a k is in good agreem e nt with the curves repo r ted by Titterton (15), Fraenkel (25), and Mu g a et al. (47). The F WHM value reported here is less than those reported by other authors. Fraenkel (s e e Figure 3) reports a FWH M valu e of 32.5 for Cf 252 while Mu g a et al. found a value of approximately 25. Titterton (s e e Figure 2) observed a F W HM valu e of 25-27 for U 235 The rather wide width reported by Fraenkel can be explained on the basis of his accidental count rate. The narrow wid t h obtain e d by this author is probably due to the lack of points between 70 and 100. This causes the exact shape of the curve in this region to be uncert a in an d therefore, allo w s selection of a so m ewhat arbitrary FWH M value. The shape of the distribu tion is very similar to the results of Titterton, with the exception of the wings. The left ~in g (small eL values) of the distribution obtained by Titterton decreased faster and to lower values than the right win g (lar g e eL value s ). The reverse is true for the distributions sho w n in Fi g ures 17 and 18. For the parity=+l case of Figure 18, the relative number of counts increases at eL 145 compared to the counts at eL = 130 and is about eq1: a l to the relative counts at 0L = 115. This variation is probably well within the uncertainties of the experim e nt. Coinci dentally, Titterton's distribution demonstrates this same ch ara c ter istic, but th e nu m ber of cou n ts in both c a ses

PAGE 84

is too small to be conclusive. See Table III for the actu al nu mber of counts obt ained at each angle. Alpha Particle Kinetic E n ergy Distributions 75 The kinetic energy distributions of the alph a particles obtained at ei g ht valu es of 6L are presented in Figures 19-22. The average values of all energies deter mined in this experiment are given in Table III. The eL = 85 angle will be ex am ined first, since this is near the peak of the angular distribution. The ener gy distribu tion for this angle is shown in Figur e 20A. The main characteristics of this spectrum are the maximum at 15-16 MeV and the FWH M of 9-10 MeV. Both cases of parity=l are the sam e This distribution is ver y similar to the uncor rela ted distribution given in Figure 16. In this instance, the peak en erg y value is probably sli ght ly less than that reported for the previous case. The avera ge ener gy value, Ea, is 15.2 MeV. This average value is sli g htly affected by the experimental lower cut-off point of 8 MeV. An examination of the distributions for lo we r OL values (70,55,~0) reveals that the peak beco mes broader while the most p r ob a ble energy value and average energy incr eas e as eL decreases. At eL = 55, the peak value is about 20 MeV and for eL = 40 the peak valu e is about 22 MeV. Actually, at the 40 angle there seem to be two peaks. One peak is of low ener gy (8-12 MeV) and the second peak is bro ad and of hi gh ener gy (15-29 MeV). For

PAGE 85

76 the oth er angles, there seems to be somewhat of a "sh e lf" in the 8-12 MeV region. r.I. 1 his "sh el f" could be due to tritons (H 3 ) released in the fission process as fi rst reported by Watson (26). About 6 triton s (12) are emitted in the fission process for each 100 alpha particles. These tritons have an ener gy peak of about 8 McV (26) and the spectru m ext~nds up to an energy of 16 17 MeV. The alpha particle detector u sed in this experim e nt would be saturated by a triton of energy 11-12 MeV. Because of the lo wer cut-off ener g y of 8 MeV, all trit ons detected would "appear" to have an energy in the 8-12 MeV range. This is the region ov er which the "shelf" occurs and, therefore, it seems likely that this "shelf" is due to triton s At e 1 = 40, the "shelf" has become a separate peak divided by a 3 MeV region from th e definite hi g h energy alpha peak. Assti ming this "shelf" or lower peak to be du e to tritons leads to the conclusion that the number of tritons relative to the number of alpha particles emitted in the fission process increases at angles close to the direction of one of th e fission fra gments It would be interest i n g to check this conclusion usin g a particle identifier (6E-E counter telescope) in coincidence with a fission fra gme nt detector at small an gle s. Simjlar trends are sho w n by the alpha particle ener gy distributions for large B 1 values (115,130, 145). Two peaks are also shown for B 1 = 145.

PAGE 86

77 The eL = 40 and BL= 145 an g les are also of special inter e st for another reason. Wh e n the parity is changed at these angles, there is a considerable rearran g ment of the number of events in the distributions. As previously discussed, this is caus e d by a chan g e in the designation of which is the light fission fra g ment after the fragment masses have been recalculated usin g the new parity. Those events which change from eL = e to its complementary angle eL = 185 e with a chan g e in parity are the ones in which the masses of the two fission frag ments were in the symmetric region. For the events collected at the experimental angle e = 40, substantial numbers switch between eL = 40 and BL= 145 when the parity value is ch a n g ed in the calculation. The alpha particle ener g y of these events is generally hi g ~ as can been seen from the shift in the peaks and in the average alpha particle energy (see Table III). This indicates that for the events in which alpha particles are emitted at small angles with respect to one of the fission frag ments, symmetric or near-symmetric fission is enhancc:d and the alpha particles from these enhanced events are of high kinetic energy. The low energy peak (assumed to be due to tritons) is essentially unchan g ed by this inversion of parity. It should be remembered that at these extreme an g les the mass value of a fission fra g ment may ch a n g e by 10-18 amu with a chan g e i11 parity. Therefore, the

PAGE 87

78 fragments need only be near-symmetric in order for the light and heavy fragments to change designation. It can be concluded from the previous discussion that for the events in which the alpha particles are emitted at extreme angles (close to one of the fragments), the alpha particle energy is high and tends to increase in energy as the angle becomes more extreme. Also, for these extreme angles, near-symmetric fission seems to be relatively more frequent than in the case of LRA emission at angles near 90 with respect to the fragments; this topic is discussed in more detail in the Fission Fragment Mass Distribution Section. Accidental coincidence events are a source of concern at the extreme angles where the actual triple coincidence count rate is low. Accidental events due to scattering are highly improbable since any possible scattered particle (fission fragment, U 235 F 19 et~.) should be stopped by the 7.91 mg/cm 2 Ni foil in front of the alpha particle detector. Although the calculated accidental count rate is only about 1 every 14 hours (these are accidental events due to an alpha particle from a LRA event and fission fragments from a binary event), this may be as high as 20-25 percent of the total triple coincidence count rate at the extreme angles. However, random triple coincidence events should have an alpha particle energy peak of around 15 MeV, since this is the most probable alpha particle energy. As can be seen from

PAGE 88

Parity := 1 10 _, < > ex: LU 8 .... z > ., ::ac ex: 6 LU 0.. .,, .... z 4 LU > LU LL C> C> 2 z i I I I I 8 1 2 1 6 20 E a ( M e V ) ( A ) eL = 55 ( B ) eL ::: 40 Parity=-1 9 8 _, < > 7 c:: LU .... z 6 > ., ex: 5 LU 0.. .,, 4 .... z LU > UJ 3 LL C> 2 C> z 8 1 2 1 6 20 E a ( MeV) I I 2 4 2 8 I 24 2 8 8 I 1 2 1 6 20 E a (M eV) 24 7 9 1 2 8 Parity=+l -r JU 1J J ~-,7-r-rT-r 8 1 2 1 6 2 0 2 4 2 8 E a (M e V) Fig 1 9 -Aloh a oarti cl e k in etic ener~y distribution fo ~ e L = 5~ 0 and 0 1 = 40

PAGE 89

-' <( > 0:: 1 0 0 8 0 z > "' ::;; o:: 6 0 w 0.. V, 1z 4 0 w Le. C) 20 4 2 _, 36 <( > 0:: w 30 > "' ::,; 2 4 0:: w 0.. 1 8 z w > w 1 2 C) z 6 Fi g P ar ity ==1 I 8 1 2 1 6 20 24 28 E 0 (Me V ) ( B ) eL = 7 0 Parity=-1 i i 8 1 2 1 6 20 2 4 28 E a ( Me V ) P a rity ==+ l I 8 1 2 1 6 20 E a (M e V) P ar i ty=+ l ~11 r-r-r I I n lJ I 8 1 2 16 20 E 0 (MeV) 80 24 28 24 28 20 -Al oha narticle kinetic ene rgy distributio n for 0 1 ~ 85 and e 1 = 10

PAGE 90

18 ..J 1 6 <( > er:: 1 4 z > 1 2 ., ::E 1 0 0.. UJ LL 6 C> 4 z 2 5 ..J <( > a:: 4 UJ ..... z > "' ::E 3 a:: UJ 0.. UJ LL C> C> z Parity = 1 8 1 2 1 6 20 E a ( Me V ) ( A ) e L = 1 00 ( B) e L = 115 P arity=1 i I I I I B 12 r I I I 1 6 20 E a p'.e V ) 24 2 8 I I I I 24 28 81 P a rity = +l 8 n __ r-r-.--r-; r12 1 6 20 24 28 E a ( Me V )' Pn.r l ty==+l F i g 21 .AJ pha p a rticle kinetic en ergy d istribution for e L 1 00 and B L = 1 15

PAGE 91

..J 3 < > oc: w ,z > ., ::;, 2 a: "--' n.. "' ,z w > w u.. 0 0 z 5 ..J < > oc: u; ,4 z > ., :IE 3 oc: w a. "' ,z: w > 2 w u.. 0 0 z '" Parity=-1 .... I 8 1 2 I .... I 1 6 2 0 E a ( MeV) (/\.) e 1 = 1 30 Parity == -1 JL I I 8 12 1 6 2 0 E a ( Me V ) .... I 24 2 8 I I 24 2 8 P ar ity = +l n I 8 12 I 1 6 20 E a ( M e V ~ P ar ity=+l 8 1 2 1 6 2 0 E a ( Me V ) 82 .... .... ~ I I I r2 4 28 24 Fi ~ 22 .Alph a particle kinetic ene rgy distr i but ion for 0 = 1 10 ard 0 = J fi~ 0 L ... L .,;

PAGE 92

83 the alpha particle ener gy distributions at these extr eme angles, th er e are some events in this energy re gi on, but their number is not lar ge If any of the events were to be selected as accidentals, these would be the likely candidates. Thus a qualitative accounting of included accidental events would not affect the preceding conclu sions appreciably. Fission Fra g ment Kinetic Energy Distributions The kinetic energy distributions of the fission fragments from LRA fission are presented in Figures 23-30, Jl e avera ge li g ht fra gme nt kinetic en e r gy (EL), the average heavy fra gme nt kinetic energy (E 8 ), and the average total fission fra gme nt kinetic energy (EF) are listed in Table III for each of the eight values of BL for which data were collected. For each of the fis sio n fragment kinetic energy distribu~ions, the sin g les spectrum of the two fission fra gme nt detectors were combined in order to present the entire fission fragment kinetic energy distribu tion on one graph. This allows a useful comparison to be made with binary data. The dashed line represents the single fra gmen t kinetic energy distribution for binary fission of U 235 which was determined by Milton and Fraser (43). Since the values of Milton and Fraser were used in the calibration procedure, this bin a ry energy distribution is the sa.'1 1e as obtained in this experi men t. The dist rib ution for B 1 = 85 (s ee Figure 26) will

PAGE 93

84 be discuss ed first. The LRA and binary distribution s are similar in all their main f eat ur es The hi gh and low energy peaks, ho wever are narrower for LRA fission. By determining th e p eak value at full width three fourths maximum, it can be se e n from the grap h th at the most probable li g ht frag me nt energy () is 91.0 MeV and the most probable heavy frag me nt ener gy () is 64.0 MeV. This is a shift in the most probable energy of the light and heavy fra gment peaks from the correspondin g value s for binary fission by 6 = 8.8 MeV and 6 = 4.4 M eV respectively. If in LRA fission the sum of the most probable light frag me nt energy and the most prob able heavy fragment ener gy ( + ) is assumed to equal the most probable fission fra gment ener gy (), then the shift in this value fro m the binary value is 6 13 MeV. This sum gives a most probable total kinetic energy of the fission fragm e nts to be 155 MeV. This is the same value given by Schmitt et al. (33), As a result of the unequal energy shift of the light and heavy fra gQent peaks, the total distribution for LRA fission is narrower than the binary distribution. The valley betwe e n the peaks is also shifted to lower ene rgy in LRA fission by 6-8 Me V. The characteristics of the most probable energy values at e 1 = 85 are also true for the average ener gy values of Table III. The shifts in tr.e avera ge en ergy of the light and heavy fra gment peaks for LRA fis s ion from the corresponding v alues for binary fi ssi on are tE 1 = 8.8 Mc V

PAGE 94

85 and A~H = 3.0 MeV. The avera ge total fission fra gment kinetic energy (EF) is 155.8 MeV. These values are very similar to the most probable values and are more ea sily and accurately determined than most probable valu es Therefore, throughout the remainder of this section average energy values will usu a lly be discussed rather th a n most probable values. The values and peak shifts obtained here are in agreement with those obtained by other investig ators (18, 25,30,33). However, Schroder (18) found the difference between the shifts observed by the two peal c s (A~L 6E 8 ) to be only 1.5 Me~ while in this experim ent the difference between the shifts js 5.6-5.8 Me V, dependin g upon the parity. This could be due to the calibration procedures used, since Schroder did not use a mass-dependent cali bration. As angles other than eL = 85 are examined (o mitt ing e 1 = 145 for the moment), the most impr ess ive charac teristic of both the distributions and the average energy values is their consistency. The avera ge energy values all remain within 2 or 3 MeV of their values at O = 85. L These slight variations of EH and E 1 can be explained easily by a purely kin ema tical argument. If the alpha particle is detected in the g eneral direction of the light fission fra gmen t (e 1 < 90), it should have given the heavy fra gment a larger recoil momentum (Coulomb repulsion) than the li g ht fragm ent It would, therefore,

PAGE 95

TABLE III AVERAGE KINETIC ENERGY VALUES FOR LRA FISSION Parity Angle Number E E EL EF E a H T eL of Events (MeV) (MeV) (MeV) (MeV) (MeV) ?ariti=-1 40 66 19.2 69.6 86.8 156.4 175.5 55 94 18.5 66.9 87 .2 154.l 172.6 70 392 15 .5 65.5 88.9 154.4 169.9 85 814 l 5. 2 65 .2 90.6 155 8 170.9 100 163 1 7 .7 62.2 92.3 15L ; 5 172 .2 115 22 19.2 63 6 92.2 155.8 175.0 130 14 17.8 63 .0 94.4 157.4 175.1 145 19 14.1 65 .7 99.1 164.8 17 8 .8 Parity:::+l 40 52 18.6 66.5 90.4 156.9 175.6 55 92 18 .5 66.0 88.8 154.8 173.2 70 389 15 .5 64.9 89.7 154.6 170.1 85 814 15.2 65 1 90.7 155.8 171. 0 100 163 17.7 62.3 92 .1 154.4 172.l 115 25 19.4 65 .5 89.2 154.7 174.1 130 16 18 .1 64 6 89 .9 154 .5 172.6 145 33 17.0 72.6 88 1 160.7 177.8 0::, CJ'\

PAGE 96

87 be expected that EH would increase at these angles com pared to its value near eL = 90 and EL would, lik ew ise, decrease. When the alpha particle is detected in the direction of the heavy fra gme nt (0L > 90), it should have given the lar ger recoil mo ment u m (Colomb repulsion) to the light fission fra gme nt. In this case, it would be expected that EL should show an incr ea se when compared to its value near 90 and EH a correspondin g decrease. These expectations are verified by Table III. At eL = 145 for parity = -1, EH increases when it would be expected to decreas e and ~L increases by a larger amount than would be .expe cted. This can be explain e d on the basis of a few accidental events bein g jncluded at this an g le. The fission fr agmen ts from the se accidental events would be fra gme nts from a bin ar y fission and, more than likely, po ssess gre ater ener gy than LRA fission frag ments. This would th e n explain the peculiar behavior of EH and EL for this angle and parity. For parity=+l at eL = 145, the results are opposite to the expectations from the kine ma tical ar g ument. The key to this situation is found in the shift of events fro m e 1 = 40 to e 1 = 145 when the parify was ch a nged. As previously discussed, these events are near-sym metr ic fission events and the energy of both fragm e nts should fall somewhere in the valley betwe e ~ the he a vy and light fra gme nt peaks. This would incre ase the value of EH and d ecrease the v alue of E 1 as i s obse r ved. The fission fra gme nt kin e tic ener gy

PAGE 97

88 distributions for 0 1 = 40 and 0 1 = 145 also substantiate this explanation. The average total fission fragment kinetic energy (~F) is amazin g ly constant for all of the e 1 values with the exception of 1115. Once again, this behavior at e 1 = 145 is explained on the basis of accidental events. This constant average total fission fragme n t kinetic energy indicates that the average separation distance of the fission fragments at scission (B) does not vary with the emission angle of the alpha particles. As was dis cussed in Chapters II and III, Halpern (34) concluded from the reduction of fragment kinetic energy in LRA fission that the configuration of the fragments at scission is more elongated in LRA fission than in binary fission and esti mated Bin LRA fission to be 13 percent greater than 5 in binary fission. From the observations here, it appears that this increased value of Bin LRA fission is constant for all angles of the alpha particle emission. From this, it is concluded that the alpha particle release mechanism in LRA fission remains unchanged as the emission angle of the alpha particle varies. While the average total fission fragment kinetic energy remains constant even for extreme angles, the average alpha particle ener g y (Ea) increases at these angles. Although 5 remains constant, this indicates that when the alpha particle is e1nittcd at extre m e an g les, it is released from a point closer to one of the fra g ments

PAGE 98

12 ;:;_ 10 > cc UJ .... z > 8 "' ::E 0 ;,:: .... 6 er UJ D.. en .... t'; 4 > UJ LL. 0 c;; 2 z 9 -' < 8 > cc LU 7 > 6 0 ;,:: .... 5 C: LU D.. en 4 .... z UJ > 3 LU LL. 0 2 0 z 30 40 / I 50 I I I (A) Pa ri ty == -1. ( B ) Parity =+ l 30 40 50 I I I 1\ I \ I \ I \ I I I / n I \ \ \ \ \ \ \ \ I ~/ I I I I 60 70 80 90 100 I FRAG ME NT KI NE TIC E NERGY (M e V) I I / \ 60 70 80 90 100 FnAG MENT K! N ETIC E NER G Y (M e V) \ I i \ I I I \ I \ I \ \ 89 ) "' :.:Q. __ 110 120 130 110 1 20 1 30 Fig. 23.Fission fr agme nt kinetic en e r g y distrihution for O l1 o 0 L

PAGE 99

90 (" I \ _, I \ < 16 \ > I a: w I ..... z 14 I > \ "' ::E 12 / C) 3,, ..... 1 0 a: w Q.. I Cl) 8 \ ..... \ I I z w \ > 6 I LLI I .... I I \ C) 4 I 1o \ C) I I z I 2 \ / '\. ,,, ~ q __ I I 30 4 0 5 0 6 0 7 0 8 0 90 1 DO 11 0 1 20 13 0 FR A G MEN T K I N ETI C EtlERGY (MeV) (A) Parity::::-1 ( B ) Parity:=+l f' I \ _, < 1 6 > a: w ..... z 1 4 > ., /::E 1 2 \ C) I 3,, \ ..... I a: 10 \ w f \ CL Cl) 8 \ ..... z \ UJ \ > \ w 6 ) .... \ C) \ I 4 0 L I z 2 \ I D '_/ --~-i---,I --,---......J'-'---r----~L30 40 50 60 7 0 8 0 90 1 00 110 1 2 o 130 FRAG MEN T K I NE TIC EN ERGY (M e V) Fi g 2 4 -Fi ssion f ra ~m ent kinetic ener g y distribution f or 0. =-= 55 l-1

PAGE 100

75 > a: UJ ..... z > 60 ., :E 0 3= ..... cc: 4 5 UJ 0,: UJ ..... z 60 > ., :E 0 3= ..... 45 0,: UJ UJ LL 0 0 15 z 30 40 50 ( A ) P ar i ty== -1 ( B ) Parit y,,, +1 I I \ \ \ I '~ I I I I I I \ I t I 60 70 80 90 100 I I FRAG MEN T K I N ETIC E NERG Y ( Me V) \ \ I \ \ J \ j / \ I \ I i 17 i I I ,.---, I I / I \ I I \ \ I \ I \ I \ \ I \ \ \ \. '--110 120 \ I I \ \ \ \ 91 130 l_l -'---...--'-'l-~~ .. 30 40 5G 60 70 80 9 0 1 00 110 1 20 FRA GM ~ NT KINETIC EN ERGY ( Me V) Fig. ;?5 --Fissi on f ragm E, nt k:lnet:tc enerr-y di s tr:tbutio n fo r 0. = 70 L 130

PAGE 101

140 ..., "" > 120 ,z 100 ::;; C) ;,,, ,er UJ 0.. .,, ,z U.1 > UJ LI.. C) C) z _, "" > 80 60 40 20 140 e; 1 20 z 100 C) ;,,, ,er 80 Lu 0.. .,, 60 UJ > Lu -:i 30 40 50 (A) Parity=-]._ ( B) Par-ity~ .: +J I 60 70 FRAG M ENT \ \ I 80 KINETIC I I I I 90 I I E NER GY ( Me V) I I I I I I I \ I \ I 100 I \ \ \ I I I I I \ \ I I \ \ r=11 0 \ I I : :: ; L.--.~ +'---.----,------,c----r---r'/ \ ----r-=;:30 40 50 60 70 80 90 100 110 FR AGMENT KINETIC EN E.R GY ( MeV) 12 0 120 Fig. 26.-Fi s sion fr a rm ent kin e tjc ene rg y distribution fo r 8 == 85 '.> 1, 92 130 I 130

PAGE 102

30 _, 25 < > cc: UJ Iz 20 > "' ::;; 0 3= I15 cc: UJ 0. .,, Iz 1 0 UJ > UJ LL 0 0 5 z 30 25 > cc: UJ 1z > 20 UJ 0. .,, I10 > .. LL 0 5 z / 30 40 50 (A) Parity = -1 ( B ) Pa1 ity =+ l \ \ \ \ \ u I I I I I I I I ,,.._, I \ I \ \ 60 70 80 90 100 FRAG M EN T KINETIC E NERGY (M e V) 11 \ I \ \ \ \ n (\ I \ I \ \ I I I \ \ \ \ \ \ I \ \ 11 0. \ I \ I I I \ J \ 93 1 20 I r / i .. ...,. l __ r=;i]; / ---.--,---Jl-,,,_u_\_ .,, _/ ,-----.--~=i-13 0 30 40 50 60 70 80 90 100 110 120 130 FRAG M ENT KI N ETIC E NERGY (Me V ) Fi g 27 -Fis s i on fr agme nt kin e tic ener gy dist1 1 ibution f or 0L :,: H JO

PAGE 103

_, <( 4 w ,_ z > ., !:E 0 3= ,_ a:: w Q.. 3 2 z w > w ,.._ 0 1 0 z _, ;; 5 a:: "'-' ,_ z > 4 ., 0 3= ,_ a:: 3 w Q.. .,., ,_ z 2 w ,.._ 0 ~1 17 I I 30 40 50 (A) Parity= -1( B ) Pa r ity= +l 94 ., I \ I \ I \ I \ I \ ,,--;::_ ;\ L I I \ \ I I \ I I I \ i I I \ I I I \ I I I \ \I I ~ \ ~ \ I ...__ / ~I I I I I I I I 60 70 8 0 90 1 00 110 1 2 0 13 0 FRAG MEN T KIN E TIC E N E RGY ( M e V ) ---.... \ -7 \ / I \.,. I I I '\ \ \ \ l \ I n I I / ,._, \ Q '-r-----,. --'-'.L-4---.,-----. ....... ---. --l--,--wc_,,_-,-30 40 50 60 10 80 9 0 too 110 1 20 1 30 FRAG ME NT KI NE TIC E NER G Y ( M eV) F i g 2 8 .F i ss i o n fr ag m e nt kin e tic ener g y distri b u t i o n f o r er = 1 ] 5 LJ

PAGE 104

_, <[ > 0:: 3 UJ 1-z > Q) ::E C> 3= ,_ 2 0:: UJ a.. "' ,_ z UJ > UJ ~1 C> z _, 5 <[ > 0:: UJ ,_ 4 > Q) ::E C> 3C ,_ 3 0:: Lo.J a.. "' ,_ z 2 UJ > UJ LL C> C> z 95 f \ I \ I I I I 7 \ I \ I \ / \ \ I r,-/ '\ j[ I I I \ \ / \ \ \ I \ \ 'i I J \ I I \ I I \ V _./ \ / "/ -I I I T --,-r 30 4 0 50 60 7 0 80 90 1 00 110 120 FR AG M ENT K I NE TIC EN ERGY (M e V) ( A ) Parity::.:1 ( B ) Parity=+l (' i \ I \ \ I I \ \ I \ i "I I I \ I \ I \ I \ I I I \ \ \ i \ \ I I / '\, / I I I 30 4 0 50 60 70 8 0 90 100 110 120 FRAG MEN T KINETIC ENERGY (M e V) Fi g 2 9 .F5 ssion fr agme n t ki netic e nergy dis ~ ribu t ion f or or,::.: 130 I 1 30 r 130

PAGE 105

.J < 4 UJ ..... z > ., ::Ee3 0 3: ..... a: UJ a.. ~2 z UJ > UJ LL 0 1 0 z .J < > ~6 ..... z 0 ;;r= ..... a: 4 UJ a.. w 0 z / / / I I / / I I I I I .... \ \ \ \ 96 I r\ I \ I I \ I I I _\ I I I I \ \ \ I -.----,------r_........_..._.,.. l __ -+__,__,_-+--'--'--'--t---r,-'-'---r:-'--', ~ 30 40 50 ( A) Pari ty=1(B) Parity = +l -,--30 40 I / / 50 60 70 80 90 100 110 I I I 7 I FRAG MEN T KINETIC ENERGY ( Me Y) \ \ \ \ \ \ I I L I 1 r\ / \ i \ \ I I I \ n 120 130 Jl~-,-----, '-/ 'l I --..----__.._,_1 __ ~ --,.-' -60 70 80 90 100 ilO 120 130 FRAG ME NT KINETIC E NERGY (Me Y) Fig. 30.-Fis s l o n fr agmen t ki netic en ergy distribution f Or 8 T ::: 111 J O .lJ

PAGE 106

97 and then receives a greater Coulo mb repulsion from this fragment which results in increa se d energy for both the alpha particle and fission fragment. This could, however, be explained on the basis o f high initial release energy and extreme initial release angle for the alpha particle. Calculations (36,49) do not support this explanation since they indicate th at the initial release energy of the alpha particle is small. Total Kinetic Energy Distributions For binary fission, the total kinetic energy distribution (43) is a Gaussian curve sy mme tric around 167.7 MeV and with a FWH M of 26.5 MeV. The total kinetic energy (alpha particle plus fission fra gmen ts) distribu tions for LRA fission are presented in Figur e s 31-38 for the ei g ht values of BL. The dashed line represents the standard distribution for binary fission. The LRA distributions for BL values of 70, 85 and 100 are very similar to the distribution for binary fission with the exception that their FWHM values are less and the LRA fission distributions are shifted to hi ghe r ener g ies by a few MeV. The distributions for the other o 1 values even resemble a Gaussian curve (except for the e 1 = 145 data which appear slightly skewed), althou gh the sta tistics are small. The avera ge total kinetic energy (ET) for e 1 = 85 ( s ee T ab le III) is about 171.0 MeV. Sinc e ET in bin ary

PAGE 107

.J ct 1 2 w .... z ';; 1 0 ::E CJ 3= .... 8 a: w a.. (/) 6 ,., > w :; 4 CJ z _, <( > 2 1 2 .... z 0 3= .... a: Lu a.. "' .... z UJ > UJ ..... 8 6 CJ 4 0 z 2 I I I I I I I I I I I I ,." I \ I \ \ \ \ \ \ \ \ \ \ \ / '-r---,-..'----,./ / ~.L-.+-.1.....l...-r----r-_.i....Li 1 '' i2o 1 30 1 40 ( 1 \ ) Parity "' -1 ( B ) Parity == +l / / 1 50 1 60 17 0 1 80 1 90 I I TOT AL KI NE T IC E NERGY (MeV ) / I I I I I I \ \ \ \ \ \ \ \ \ \ 200 98 .nlU 21 0 220 ----.-, ---.--! _n __ ,,_I ~~~--~--~ '--.-----,,-[L 11 1 2 0 1 30 1 40 150 160 1i0 1 80 1 90 200 2 10 220 TOT A L KI NET IC E NE R GY (MeV) Fig 31 .-Tot aJ kinetic ene r g y ( a l p h a particle pl us f ission f'ra e; : mer,t s) di s trl bu.tj 0!1 for O 1 =c 4 0 J

PAGE 108

99 ~ -------------------------------, ---' 18 0:: UJ ,16 z > 14 ., ::E C) 3:: 12 ,0:: w a.. l 0 (I) ,z LU 8 > w "-6 0 0 z 4 2 ---' 1 8 0:: w 16 ..... z > 14 ., ::E 0 3:: 12 ..... 0:: w 10 a.. "' ..... z 8 w > w "-6 0 C) z 4 2 120 130 140 I / / ( A) Parity=-1 ( B) Parity::!+l I / / I I I I I I I I I i I / I \ \ \ \ \ \ \ \ 1 50 160 170 180 190 I I I TOTAL KINETIC EN ERGY (MeV) I I I I I \ \ I \ \ \ \ \ \ / l_~ 200 21 0 iJ 1 20 130 140 l 50 160 170 180 1 9 0 200 210 TOTAL KI NE TIC E NERGY (M e V) Fi g 32.-To tal kin et ic en e r gy ( alpha ra r ticle plus fi3 s i on fr arme nts ) distribution for e L = 55 220 220

PAGE 109

_J 50 <( > er w ..... z > 4 0 ., ::E 0 3= ..... er 30 w ,,_ C,? ..... z w 20 > w LL 0 0 10 z _, 50 < > er w ..... z > ., ::E 0 3= ..... er LLJ ,,_ C,? ..... z w > w LL 0 0 z 40 30 20 1 0 ,------------------------/ / I I I I I I I I I I I I I \ \ \ \ \ \ \ \ 100 1~ --.,...----,-~~~-~-------,-,---,.---,----,---'--,,---,---11 2 0 130 140 150 160 170 18 0 1 90 200 210 220 TOTAL KINETIC ENERGY (MeV) ( A ) Parity=-1 ( B ) Parit;y==+l / ...... / \ I I \ I \ I I f \ I \ I \ I \ \ / ,/ j ~ \ \ ls-Lr] '~ I I T I -r 120 130 140 150 160 170 1 80 1 90 2 OD 210 Z20 TOTAL KINETIC E NERGY (MeV) Fi g 33 .Total kin c t::_c ener gy ( alph a particle plus fi ssion fr ag m e nts) distribution f or e 1 = 70

PAGE 110

101 90 -;;_ 75 > a: UJ ..... z > 60 :E 0 ;oc ..... a:: 45 UJ Q.. en ..... z 30 UJ LL 0 15 / I / / I I I I I I I \ \ \ ........ --------..----'----,---'--.----.----...-----:-. ----,--~ : p -r--120 130 140 150 160 170 180 190 200 210 TOTAL KINETIC ENERGY (MeV) (A) P ar"ity~ -1. (B) P ari ty=+l 220 -----------------------, 90 ;; 75 > 0.: UJ ..... z > 60 ., ::E 0 ;oc ..... a:: 45 UJ Q.. en ..... z 30 UJ LL 0 0 15 z I I I I I I I I I I I t: l \ \ / --.--~-----, .--~/ -.--~~~ ----,--C7 .---,----..,.,----,-, -'--11 _,_ ---,-------;-' 120 130 140 150 160 170 180 190 2 00 210 TOTAL KINETIC E NERG Y (M sV) Fi g 34.' l'otal kin et :i c energy ( alpha particle n )u s fis s ion f r ag m P nt s ) ctistrioution for e 1 = 85 220

PAGE 111

_, < > 0:: w -z > ., ::E C> "" -0:: w Q.. Cl) -z w > w LL C> C> z _, < > 0:: w -z > ., ::E C> 3'= -er: w Q.. Cl) -z w > w LL 0 0 z 18 16 14 12 1 0 B 6 4 2 18 1 6 14 1 2 10 8 6 4 2I / / I I I I I I I I I I I I \ \ \ \ \ \ \ \ 1 02 Jl 1. > .. ... -~ ---i-'-,-....,._ -r-----,--. --....,-. ----,. -.,..~~-r----.1 2 0 130 140 (A) P a : e i t y= -1 ( B ) Par i ty= +l I / / ---n -r 120 130 140 150 160 170 1 8 0 190 I I TOTAL KINETIC E N ER GY ( Me V) / I I I I I \ \ \ \ \ \ 1 5 0 160 170 1 80 190 TGTAL KI NE TIC E NERG Y ( M e V ) 20 0 21 0 2 2 0 200 210 2 2 0 Fi ~ 3 5 -To tal kin e tic en ergy ( alpha par ticle nlus fj ssi on f ra r,;ms nts ) distr.ibut:i .on f or e, = 100 t L

PAGE 112

_, ;: 4 a:: w ,z > 3 a:: UJ 0... "' 2 ,z UJ > w LL c:, c:, z _, < 4 UJ ,z > CP ::a, 3 c:, 3= ,a:: UJ 0... 2 z w > UJ LL C> 0 z 1 10 3 / ,,,, -~ ... \ I \ I \ I I \ I '""" \ I \ I \ I C\ I \ I \ I \, ~ i ~ I / / .,., ,,, I I I I I I I I 1 40 150 160 17 0 1 80 1 90 200 210 2 20 230 240 T O T AL KINET I C EN E RGY (M e V) ( A ) Parity= 1 ( B ) Parity =+ l .--------------------------I I I I I I / /~ \ I \ \ / / J_I l~-\ L I ( 14 0 1 50 1 60 17 0 180 1 90 200 2 i 0 T OTH K I NETI C E t;~RGY ( MeV) [ 220 23 0 240 Fi ~ 36 Total kin e ti c ener ~ y ( alpha particle plus fi ss ion fr ag nents ) distribution for e 1 = 11 5

PAGE 113

3 _, < > ~ -----/ \ I \ 0:: w .... z > I \ I \ I a, ::,;, c:, 2 3= .... I \ I \ 0:: w I \ 0 Cl) .... I \ z w > I \ I UJ u.. c:, c:, z I ~ \ ~, I \ l I / / I '' / '-, -I I I I I I I I I r 1 20 1 30 140 1 50 1 60 1 70 180 1 90 20 0 210 220 TOT A L K I NET I C ENERGY (MeV) ( A ) Parity=-}. ( B ) Parity::+l ~ --,._ _, 3 r / < I \ > 0:: \ UJ .... :z I \ > I \ a, ::,;, I c:, I 3= 2 .... I a: \ UJ I 0.. I Cl) I \ .... z I \ w > w I u.. l c:, ,, L_ 0 \ z \ I '_Lj_ '--I I 1 20 130 140 1 50 160 170 1 80 190 200 210 220 TOT AL KINE T IC ENERGY (M e V) F'ir,. 37 -T otal kin et ic e!1cr R'. v ( aJ oha Dart ic J.e uJ.us ..._ V f 1 5 si on f r agm ents) di.s tri but ion fo r 0 1 = 130

PAGE 114

--' < > n:: 4 w ..... z > ., ::E 0 3 ;,:, ..... n:: w 0.. (I) ..... 2 z w > w u.. 0 0 z 9 _, 8 n:: UJ ..... !:: 7 > ., ::F. 6 0 ;,:, ..... 5 a: w 0.. (I) 4 ..... z w 3 u.. 0 2 0 z I / / --,, I I I 120 130 140 ( A) Pa,1i ty= -1. ( B ) Parity = +l ~" / \ I \ r I \ I \ \ I \ I I I \ I \ I i I I I \~ \ '\_ I I I I 150 160 170 180 190 I I TOTAL KINETIC ENERGY (M e V) I I I I I I I I / \ \ \ \ \ 105 rll 200 210 22 0 / ......--.-~ -~~-r--, ~'----t-----r" ~l --r-"-', 1l-r--[l 120 130 140 150 1 60 17 0 1 80 19 0 200 21 0 220 TOTAL KINETIC E NERGY (MeV) Fi g 3 8 -T otal ki ne tic ener gy ( a l pha p ar ticle olus fi ssion f r2 gme nts ) d:i str i bution for e 1 =-= 1L15

PAGE 115

106 fission is 167,7 MeV, this means that the average total kinetic energy (at eL = 85) for LRA fission is 3,3 MeV higher than in binary fission. Fraenkel (25) observed a similar result for LRA fission of Cf 252 As an g les in both directions away from eL = 85 are examined, a slight increase in the values of ET is observed. Since the average total fission fragment kinetic ener g y (~F) remains essentially constant, this slight increase in Em is primarily due to an increase in the value of Ea. As previously discussed, the value for e 1 = 145 is an exception to the general trend. Since the relative frequency of LRA emission is much greater at 0 1 = 85 than for any of the other eL values us~d in this experi m ent, the average total kinetic energy sum m ed over all angles would be only sli g h t ly higher than the ET value for eL = 85. Therefore, it can be concluded that the average total kinetic energy for LRA fission is about 3.5 MeV higher than the average total kinetic energy for binary fission. Fission Fragment Mass Distributions The fragment-mass distributjons for the eight values of eL, with both positive (+l) and negative (-1) parity distributions presented.for each eL value, are shown in Figures 39-46. As before, the dashed line represents the distribution for binary fission. An examination of th e d is tribution ror e 1 = 85 (see Figure 42) will be

PAGE 116

107 undertaken in the beginning. For negative parity, the mass distribution is very similar to the binary mass distribution with the exception that the heavy mass peak seems to be shifted down by about 2 amu and, likewise, the light fragment peak is shifted slightly up by less than 2 amu. The peak values are determined at full width three fourths maximum. A more interesting characteristic of the distribution is the number of events with mass numbers 105-115 and 120-130, that is, mass numbers in the near-symmetry fission region. For LRA fission, the mass number for symmetric fission fragments from U 236 *.should be 116 neglecting prompt neutron emission. The relative yield of events in this region is defj nitely greater in the case of LRA fission than for binary fission. If the distribution for positive parity is examined, the heavy mass peak is observed to be shifted slightly to lower mass values and the light mass peak undergoes a cor responding shift to larger mass numbers. This causes the two peaks to be slightly closer together an~ thus, increases the relative yield of events in the near symmetric region. It is observed, therefore, that the distributions for both negative and positive parity indicate an increase in the yield of near-symmetric fission events for LRA fission compared to th~ yield of these events in bi~ary fission. Asstiming, as discussed pre viously, that each parity calculation is correct in about ,. half of the cases, then the "co:nect" distribution should

PAGE 117

108 show more n ea r-symmetric events than th e parity=-1 distribution and le ss of th ese events than the parity =+ l distribution. In any case, the distributions indicate that there is an increase in the relative yield of near symmetric events for LRA fission compared to binary fission. The data of Schmitt et al. (33) were interpreted by Methasiri (5) to show similar results for coincid ence betw een fission fragments and the higher energy alpha particles from LRA fi ssion. For e 1 values other than 85, th e reason that the half of the graph below mass number 116 is not a mirror reflection of the half above mass number 116 is becau s e the nu mbe r of events is totaled for a two amu interv a l. As we move away from e 1 = 85 toward more extre me an g les, it is observed th a t for at least one of the parity c alcu latj ons at each angle, there is a significant riw n ber of symmetric or near-symmetric masses in the distribution. At the more extreme angles, where the change in mass number with ch ange in parity becomes larger, the distrjbution usually shows a peak in the symmetric re g ion for one of the parity values. If each parity calculation is correct in about half of the cases, then we have a consid erable yield of symmetric or near symmetric events for LRA fissi0n at these extreme an g les. This conclusion was made e::i.rlier on the basis cf the alpha particle kinetic ener gy distribu tions and the fis sion fra gme nt kin e tic ener g y distributions.

PAGE 118

It has now been substantiated by the fra gme nt-mass distributions. 109

PAGE 119

110 10 r I I /' \ I ~ r ) I I 9 -' f I I < > t1Jl I ex: 6 UJ II z :::, 7 :,;a < 0 6 ;,:, Iex: 5 I UJ 0.. I "' I I4 z \ I UJ > \ I UJ I LL 3 I 0 \ I I I 0 2 I \ z I \ 1 70 8 0 90 1 00 1 10 1 20 1 30 1 40 150 1 60 MASS NUi : B ERS ( Ah U) ( A ) Parity= -1 ( B ) Parity = +J. 11 10 r \ I -.... I I -' 9 / \ \ < \ > I I ex: I UJ 8 \ II I I z I \ :::, 7 I ::;; I < 0 6 I .... I ex: UJ 5 0.. .,, .... z 4 L,J > UJ \ LL 3 I 1l 0 0 \ \ 2 j z j \ I I LI \ \ I 7 "' '_/' r I I 70 80 90 100 110 120 130 14 0 1 50 160 MASS NU M BERS ( A MU ) Fig 39 -Fr agm cnt~a ss dlstri b uU or. for 0 L = 40

PAGE 120

-' < 16 14 1 2 w .... z 10 0 3c .... 8 a: w 0.. ~ 6 z w > w 0 z -' < > a: w .... z => :i;, < 0 3c .... a: w 0.. "' .... z w > w LL 0 C) z 2 16 14 1 2 10 8 6 4 2 I 70 8 0 '\ I ', I \ / I / I I I I I I I i 90 100 (A) P a rity=1 ( I3 ) Paritv = +l r -, / ( I I I I I I I I / 70 80 90 10 0 I \ I \ I 1 10 12 0 130 MA S S NUMBERS ( A M U ) I I I \ i I \ I 140 (\ r -J I \ \ \ 15 0 t \ I I I I [L.J1 / r 1 10 1 2 0 1 3 0 14 0 1 5 0 MASS NUMBER S ( A ~W) Fig 40 -Fr arment mass distribu t ion for eL = 55 ll l 1 60 1 6 0

PAGE 121

60 r \ I ) I -;;;_ 50 I I > I I a: w I/ z ::, 40 :;a < I 0 I 3" I Io: 30 I \ w I Q. I (I) I II I 20 I > w LL 0 0 "L z -fI ;;;_ 50 > 0:: w 1z 0 3C 40 ,_ 30 a: w Q. (I) I20> UJ LL 0 0 10 z 70 80 90 100 ( A ) Pari ty=-l (B) Parity=+l 70 80 I J i I (' / \~ I I I I I 100 I \ I I \ n. r I "\ \ I i I I I I \ I I I I I I 11 0 120 1 30 140 MASS NU h \ BER (A M U) rI ( J \ '\ I I I I I \ I I I \ 1i ~ \ \ \ -. I 110 120 130 140 1 50 MASS NU MBER (AMU) Fi g ~1 -Fra g ment-mass distribution f or e 1 = 70 112 1 60 17 0 ) 1 6 0 170

PAGE 122

60 50 =:, ::E < 40 c,: LLJ D.. "' ..... z 30 LLJ > LLJ LL 0 2 0 C, z 10 70 60 50 =:, :s < ex: LLJ 40 D.. "' z LLJ > LLJ 3 0 LL 0 C, z 20 10 I I n I I I 1 13 : M \ 7 j I n I LJ Li I I I I I \ I u1 \ / 1 \ I // \ ~ ,----r---T ----r ---,h-r:; L -y---1 ----r. L -----70 8 0 9 0 100 110 1 2 0 1 30 14 0 1 50 l G O (A) P a ri ty = 1 ( B ) P arit y= +l r, I I \ I \ I I I I I I I i ilJ 11 .I L i--f---' 7 0 80 90 10 0 ~ASS H U M BE R ( A Ll U ) ------~ I I 1 10 12 0 1 30 MA SS NU MB E R ( A M U ) ,14 0 \ \ I I I I \ \ 1 r < \ I '--,-150 1 60 Fi g l \ 2 -F r agme n t-rn,::u .., s d j s tri b u t :i on fo r e 1 = 8 5

PAGE 123

114 .... ~ ----30 (\ ~ _, I ~ \ < / \ > I i 0:: 25 w I \ .... z I ::, I ::e I < 20 C> \ I 3= I. .... I I 0:: \ I w 0.. 1 5 I ti) \ I .... z I w I > w \ .... 10 I C> I \ C> I I z I 5 \ \ =+ \ --rn 7 f 70 80 90 100 11 0 i20 13 0 140 1 50 1 6 0 MASS NU MB ER (A MU) ( A) P ari ty=( B ) Parity=+l ---30 ( _, J '-'\ rI < I \ > I I 0:: I \ w 2 5 .... I z I i I ::, I I ::.; < 20 I I ~ I C> I 3= .... 0:: \ w 0.. I ti) 15 .... z I w > w \ .... 10 \ C> I C> z I 5 :CL c:;1.L \ \ _T[l__ 70 80 s o 10 0 110 1 20 130 1 40 150 160 M ASS NU MB ER (MIU) F i g 4 3 Fra e:r.i cnt-rna s s distr ibution for eL ::: 1 00

PAGE 124

11 5 r-, I \ I \ I '...... 1 I / \ I I ...J I < 4 \ > 0:: i L,J Iz I :::, I ::E 3 I I' I < I C) I 31:a II 0:: I L,J Q.. I 2 / J V) I II z L,J I > \ L,J LL \ C) 1 I \ C) I z I I \ I \ I "/ \ I / \ I I I I r--~ 70 80 90 100 11 0 120 130 140 150. 160 170 MASS NU MBE R (A M U) ( A ) Pa.rit. y= 1 ( B ) Par-it y= +l r, -, I \ I \ I r J \ ...J / I \ < I I > 4 \ 0:: L,J I I II i :::, I ::E j I < I 3 \ C) I \ 31:a a: I L,J I Q.. l \ V) 2 n ~ ,, J r 1 \ [ Il \ z L,J > I L,J LL \ C) 7\ 1 C) \ ~ z I I \ / _L __ I -----,I ,---,I i I 70 80 9 0 100 110 1 20 130 140 1 50 1 60 170 MASS NU M BER (A MU ) Fi g 4 4 .Fr a ~me nt mas~, dist ribut i on for e 1 = 1 15

PAGE 125

11 6 ,I\ 1"_, 4 ,__ '--, r n \ "" > I er: ( \ w I .... I I I \ :::, I I :le 3 ..L "" I I I 0 \ ;,: /. I .... I er: I I w 0en 2 .... I z I w I > I w LL I \ 0 I C: : I z 1 I I I \ I I \ I I I I \ I ~/ I / I I I I 7 0 8 0 90 100 1 1 0 1 20 13 0 140 150 1 6 0 M A S S NU MB ERS (AMU) ( A ) Pari ty=( B ) P arity::.:+ l -,-\ A 4 I '' ,-,_) \ _, ) I \ < \ > er: I I I \ w .... \ z :::, I :a: 3 < 0 ;,: .... \ er: I w 0v., 2 I .... z I w > w I LL 0 I 0 1 \ Ill z I \ 1 / I I \ -(---'T r70 8 0 90 1 00 1 10 1 20 130 140 150 1 13 0 A !ASS NUM B ERS (A MU) F.ir, 4 5 Fta e:m c:-it mas s distri but i on for 91 = 13 0

PAGE 126

_, <[ > 0:: w Iz :::, :a, <[ C, ;., I0:: IJJ 0.. Cl) Iz w > w LL. C, C, z _, < > 7 6 5 4 3 2 7 6 1z 5 <[ C, 3" ... 4 0:: w 0.. .,, 3 w > w C, z ("\ I \. J I ( i I I I I I. I I I I I I I I I I I I I I I 70 80 90 70 ( A ) F'arity==-=l ( B ) Parity=+l '!0 I I I 90 I (\ I J I 100 I I \ I I I I I \ I \ {' r J \ I I \ I \ I I I I I I i I I \ I I j -n I \ / I 110 1 20 130 1 40 MASS NU MB ERS (A MU) i \ \ I I \ I I I I I \ \ \ l 150 11 '1 \ \ \ I 1 6 0 ~ )f J ..... ....--.-: l11 0 1 20 130 140 150 1 60 MASS NU MBERS ( A M U) Fi p; l t6.-F r ag r.1ent-mas s distrib utio :1 f or 8L == 11 15

PAGE 127

CHAPTER VI CONCLUSIONS Several conclusions were drawn in the previous chapter while discussing the experimental results. These will now be summarized and elabor a ted upon in an attempt to present a descriptive model for LRA fission which correlates these exp erime nt a l results. A summary. of these results and conclusion s is presented below. (1) For th e alpha particle ener gy distribution s there seems to be a 11 shelfn, probably due to tritons, in the 8-12 McV region. At extreme angles, this "shelf" became a sep a rate peak From this b eha vior, it is concluded that the numb er of tritons relative to the number of alpha particles emitted in the fission process increases at angles close to th e direction of one of the fission fra gme nts. (2) The average total fission fr agment kinetic ener ey (EF) in LRA fission is about 155 MeV or 12 13 MeV less than in hinary fi.ss:lon. The average total kinetic energy (al pha particle pJ.us fission fra gmen ts) is sl5ght ly greater than J71 Me V for LRA fission, which is about 3.5 MeV higher than the avera ge total kinetic energy for bin a ry fission. The average tot a l fission fragment kinetic energy i::; ess entially co nstant for all alnhct oarticle emiss:l on 118

PAGE 128

119 angles an~ from this, it is concluded that the average separation distance of the fra gment s at scission (B) remains constant for all emission an g les in the LRA fission process. As indicated by EF, Bis considered to be lar ge r for L RA fission th an for binary fission. (3) From an examination of the alpha particle kinetic en e rgy distributions, the fission fra gme nt kinetic energy distributions, and the fra gme nt-m ass distributions, it is concluded that symmetric or near-sy mmet ric fission is more probable in LRA than in binary fission. The yield of these symmetric or near-sym me tric events becom es con siderable at the extreme angles. (4) From an examination of the alpha particle kinetic energy dis t ributions and the average al pha particle kin e tic energy (Ea), jt is ob se rved that the ave rage or most probable alpha particle ener gy increases with the extremity of the emission an g le. Sine~ symmetric or near symmetric fission is also favored at these extreme an g les, it is concluded that alpha particles emitted from these symmetric or ne a r-symmetric fission events are of higher average ener g y than alpha particles emitted from more asymmetric LRA fission events. (5) The observation of a constant value of Bin LRA fission for all an g les of alpha particle emission le ads to the conc]usion that the alpha particle release mechanism in LRA fi ssi on r ema ins unchan ge d as the emission angle of th e alpha particle varies. The increa sed valu e of i\x at

PAGE 129

120 extr e me angl e s indic a tes that, for e m is sio n at e x tr e m e an g les, the alpha particle is released fro m a point closer to one of the fra g m e nts and, th e refore, receives a gre at er Coulomb repulsion from this fra g m e nt which re s ults in an increased value for Ea. A model for LRA fis s ion is now be g innin g to develop. The model for the fis s ion process of Whetston e (37) seems adequate to ex p lain qu a lit a tively the observ a tions made here for LRA fission. The Whetstone model assu me s the sh a pe of the nucleus at the point of scission to rese m ble an asy mm etric 1 1 dumbbell 11 that is, two more or le s s sph e ical parts of un e qual.size connected by a thin neck. This shape is assumed to be independent of th e final ma s ses of the fra gm ents. The final m a sses of the two fr a gm e nts are determined by the point alon g the n e ck at wh i ch scission occurs. The most prob a ble point for scis s ion to occur is in the middle of the neck. This gives the most p r obable mass ratio, that is, asy m m e tric fission. Very asym me tric fission results when the scission point is n e ar th e sm a ller fra g ment and symmetric or near-symm e tric fission results when the scission point is near the lar g er fra g ment. It is hereby postulat e d that the alpha particles are emitted at or very close to the mo me nt of scis s ion and at the scission point from a scissionin g nucleus which closely rese m ble s the mod e l pro p osed by Whetston e (37). Wh e n s ymm e tric or n ea rs y mm etric fission occur s accordin g to this model, the alpha particl e should b e

PAGE 130

121 released fro m the scission point which is near the heavy fra gment Since this model considers the neck portion to be thin, it should not exert a strong Coulo mb repulsion on the alpha particle. It is also possible, as advocated by H a lpern (34), that the neck snaps b ack quickly and, therefore, exerts only a small repulsion on the alpha particle. The alpha particle would then be accelerated in a direction close to the li g ht fr avnent and with a larger than average al pha particle en ergy However, it is debatable as to which fra gment is actually the li g ht frag men t in this situation. Because of this, the distribu tions at both e 1 and 185 e 1 should show symmetric or near-symmetric fission events and incr eased alpha particle energy. This was seen to be true. This model also explains the rea s on for the increased symmetric or near-sy~netric yield at extreme angJes. For the alpha particle to be detected at extreme an g les, it must be emitted from a point close to one of the fra g ments. If the scission point were near the smaller fra g ment, very asymmetric fission would result. An alpha particle emitted from this point would be accelerated by a very small fragment in a direction toward a very lar ge fragment. In this case, the alpha particle would probably be deflected by the Coulomb repulsion of the lar ge fra gmen t and should be detected at an angle approximately perpendic ular to the d tre ction of the fragments. Therefore, ev ents of this ty pe should not be detected at extreme angles.

PAGE 131

122 The only other point fro m which the alpha particle can be emitted in ord er to b e detected at an extreme angle is close to the he avy fr agment. This lead s to symmetric or near-sy mmetric fission and explains the observed increase for this type of fission at extre me an g les. In summary, it is concluded that the LRA fission mechani sm is very similar (except for the alpha particle emission) to the bin ary fission mechanism. The Whetstone model seems to be the most appropriat e for explaining this mechanism, although it does not give a complete quantitative description of the process. Th e LRA fission results are difficult to interpret and no one model can explain all the results or describe the exact mechanism of alpha particle release. Any further inter pre tation of LRA fis si on results will be left for the theorist.

PAGE 132

APPENDIX A CALCULATION OF ACCIDENTAL 1'RIFLE COINCID ENCE COU NT RATE

PAGE 133

The equation for accidental count rate is, (Al) Where, A= 2'TR R 1 2 R 1 = singles count rate on counter 1 R 2 = sin g les count rate on counter 2 T = coincidence resolvin g ti me For this LRA f'Jssion experim e nt, th ese values are, R 1 = 2 c/sec (Y count rate) 'l'hen, Therefore, R 2 = 600 c/sec (X and Z coincidence count rate) 21" 60 x 109 sec A (60 x 109 sec)(2 c/sec)(600 c/sec) Time between accidentals= 1 7.2 X 10-s = 14 x 10~ sec Accidental count rate= 1 ev ery 3.9 hrs. 124

PAGE 134

APPENDIX B DERIVATICN OF FISSION FRAGMENT MASS EQUATION

PAGE 135

Refer to Fi gure 47 for th e follo w in g equations Ya = Ma.Vasin0 Xa = MaVa.cos8 y2 = M 2 V 2 sin8 X2 = M 2 V 2 cosB By conservation of mo ment u m ; M 1 V 1 + Xa = X 2 Substitutin g into these equations for Xa, X 2 Ya and Y 2 and by the conservation of mass l aw we have the ba sic equations with which to be gin ; (Bla) (Blb) (Blc) M 1 V 1 +Ma.Va.case= M 2 V 2 cosB Ma.Va.sine= M 2 V 2 sinB M 1 + M 2 + M 0 = M Where Ma= 4 and M = 236 for U 235 + 0 n 1 Taking the equation for kinetic energy E = !mv 2 2 Solving for V, 1 (B2) V ::, (2 E / m )2 126

PAGE 136

127 E1 Fig. 47,-Vector di ae; r am illu s tr a tin g c o n s e r v a tion of' momentum for LRA fission

PAGE 137

128 Substituting Eq. (B2) into Eq. (Bla), M 1 V 1 + MaV 0 cose = M 2 V 2 cosB l 1 1 Ml(2El/Ml)I + Ma(2Ea/Ma)I cose M2(2E2/M2)I cosS 1 1 1 (2M 1 E 1 )i + (2MaEa)i cose = (2M 2 E 2 )i cosB Squaring and dividing by 2 gives, 1 (B3) M 1 E 1 + 2(M 1 E 1 MaEa)i cosB + MaEacos 2 8 = Square Eq. (Blb) and multiply by, Into this equation, substitute E = mV 2 Adding (B3) and (B4) and then simplifying, 1 ME cos 2 B 2 2 M 1 E 1 + 2(M 1 E 1 MaEa)i cose + MaEa(sin 2 0 + cos 2 8) M 2 E 2 (sin 2 8 + cos 2 S) Substituting sin 2 B + cos 2 S = 1 and rearranging, 1 2(M 1 E 1 MaEa)i cosB = M 2 E 2 M 1 E 1 MaEa Squaring both sides, (B5) solve for ~ 1 : Substitute M 2 = (M-M 1 -Ma) into Ea. (B5),

PAGE 138

129 ltM1Elr '1a I~aCOs 2 0 -~ (M-M -M ) 2 E 2 -2(M-M M ) EM E 1 a 2 1 a 2 a a + 2M 1 E 1 MaEa + M~E~ + M:E: 2(M-M -M )EM E 1 a 2 l l Multiplying the terms a nd rearran ging M:Ei + M~E~ + 2E 1 E 2 M: + 2MaE~t\ 2 ME !M 1 + 2E 2 MaEaM 1 + 2E 1 MaEaM 1 2 ME 2 E 1 M 1 + 2MaE 1 E 2 M 1 4M EM E cos 2 B + M 2 E 2 + M 2 E 2 2MM E 2 1 1 a a J 2 a 2 a 2ME ME + 2E M 2 E 2 + M 2 F 2 = O 2 a a 2 a a a Ja Combining of terms and factoring gives, (E 2 + E 1 ) 2 M~ [2( M-M a)E: + 2( M-M a)E 1 E 2 2MaEa(E 2 + E 1 ) + 4MaEaE 1 cos 2 B] M 1 + [(M-Ma) 2 E! 2(M-Ma)E 2 M E + Mc,_ 2 Ea 2 ] 0 a o Finally we have, (B6) (E 2 + E 1 ) 2 M~ {2(E 2 + E 1 )[(M-Ma)E 2 MaEa] + 4MaEaE 1 cos 2 B}M 1 + [(M-Ma)E 2 MaEa] 2 = 0 This equation is the general equation for M 1 It is a quad ratic equation and can be solved by the quadratic formula. (B7) M 1 :: 1 -b (b 2 4ac)2 2a a=(E2+E1)2 b {2(E 2 + E 1 )[(M-Ma)E 2 MaEa] + L iM aEo:E l cos 2 0}

PAGE 139

APPENDIX C COMPUTER PROGRAM FOR ANALYSIS OF LRA FlSSION DATA

PAGE 140

C REDUCTIU~ OF TER~ARY ALPHA-FISSIU~ DATA TO MASS-ENERGY C 1ST Ii'JPLJT = TOTAU : 7 EL, EH, ALPH/~M, Ml.i'~UM.J C 2 N D l NP u T = A K ,\ K P F3 K BK 1) C 3RD INPUT= DELTAE C 4lH ;\ PUT = .'JSFTS, Alf>H ,\ C 5 TH I.\ PU f = C X l C X H CY E 7 8 C Y 6 7 7 C ZL CZ H N Cf\ RD C TIME3C, X~ATE C 6 T H l r~ P U T = D t: TR ( 1 J ) D E T R ( 2 J ) D E T R ( 3 J ) E T C DIMENSIC~ CUUNTC(3Cl,CUUNTN(30),CRATEC(30),CRATEN(30), l C XH { :rn ) C XL ( 3 0 l CY 6 7 7 ( 3 G ) CY 8 7 B ( 3 0) CZ L { 3 0} CZ H ( 3 0 l 2 E: N X ( 1 0 )' OE I 1 ,: ) K T ( 3 0 .) ) K E TC ( 3 :-, ) l r: EX ( l SO ) 3 K E X C ( l 5 C 1 ) K t Z ( l '> 0 ) K E Z C ( 1 5 0 ) t ~ X D S T C ( 2 5 0 l M X D S T R ( 2 5 0 l 4 t-' Z C :, f C ( 2 5 0 ) M Z D ST R ( ? 5 C l r-J CA k D ( 3 l l i,J :: V E i'i T ( 3 1 ) 5 NO( lCOO), TlivlE3D( 3")) ,XCuUf\JT( 30) ,IRATE (30) DJ r,,i E ; ~ S Hn DETR ( 3, l CO 1 ) l X Mt\ S S ( 2 10 J f) ) Y KE ( 5 S 2 ) 1 YKEC(50,2),ZMASS(2,1CCO) D I ME N S I L : J E N ER G Y ( 2 't 1 C O 0 ) COMMUN DELTAE(280) 5 KEAO (5,6) TOTl' LM, El, EH, t1LPHAt-:, MXNUA\J 6 FORMAT (~FS.1,15) C TOU U = MASS I\JO. CF FISSIO ,' JI !\JG i~LCLCUS C EL, t:H = MOST fJRJb/d3L F EJlcRGY fJF LIGHT Ai'H) HEAVY C H~AGME~HS, ~:ESP. C ALPH;\t/; = MASS rm. OF /1LPH,-\ Pt,RTICL[ C M X MJ ;\ ;\ = NO., U F D IF i-< R:: 'JT Ail G L:: S F CJ~ UI IC H O /:, H. I S T /1, KE i\J 7 i{E/.1 D (S,::3) t\K, AKP, 8K, r,KP 8 FOkM~T (4FL0.5) C A K ;, :<.. P J K 3 i<. P = SCH M I T T S SU 3 CU,~ S T :\ J l S F CR C ::. L I 3 ,z A T I O 1'. C SCHE~~ 9 10 C C 11 12 13 14 15 16 17 18 19 2') 21 C C C 22 23 24 25 R E /1 D ( :> t ,J ) D I: L T A L FO ~ i''i=~ T (2'.J(F3.l,1X)) OELT~0 = AR~AY hHICh GIV~S ENERGY LOSS UF ALPH~ PA~TICL~ I~ NICKEL FUIL 00 14 L=l,?) AL= FLJ '\T(Ll YKE(L,1) = 7.5 + (AL/2.0) YKEC(L,ll = 7.5 + (AL/2.1) DO 16 I=l,LiOO 'JO(Il =[ DU 410 KA=i,~XNJAN MI:-;;~c = 1 l"lAX.\C = J FORt'.>~l ( I 10,F lG. l l NSETS = \JC. St~TS OF LAff, T/1K'. ::N ,\T,.,t \lGLE=t,LPt1/.., /~ND FCR ,nJ!CH fJIFF~R d, f Ct.LIL\; h AC = 1 E 5. C, ALP h COS!~: CCS(~LPH~~) \D~LT~ = NSEfS + 1 131

PAGE 141

2 6 i Cl\ R fJ ( 1) = 0 2 7 i~ 0 [ V TC = 0 28 DO 65 N:2, N D E LT~ 132 C EACH PASS Tl-i 1 ~U THIS DO LOOP COVERS l SET (Jf Ot1TA C C C C C C C C C C C C C C C C C 29 NFK = i~-1 3 ') R E .A D :i 3 1 > c x u ff K > c x ;1 r,; F K l c Y e 7 a ( rJF K l c Y 6 n P~ F K l 1 C Z L ( t,; F K ) C Z H ( ;~ F !<_ ) > ~ C A R l) ( N ) T I M '.-: 3 Q ( N F K ) X F\ A T t: ( N F I< ) 31 fORMAT (2F5.0,2F5.1,2F5.0,T41,15,T51,F5.2,F5.0) 32 33 34 35 36 37 38 39 40 CXL,CXH,CZL,CU~ = C/1.LIBRATIC t ~ PUPHS FOR LIGHT AND HEAVY fRAG~ENT OF X,Z INPUfS RESPECTIVELY, FUR EACH i\SE r u.i-1 J CY878, CY677 = CALI B RATION POINTS FOR TH-22 8 ALPHA CALIBKATICN SCURC~. THE 8.78 MEV PEAK IS FROM P0-212 ANO TH~ 6.77 ~EV P~AK IS FRU~ P0-216 NCA~D(Nl =NU.DATA CONTAINI N G CARDS IN NSET(N-1) TIM~3C = TIME 0~ 30, IN HOURS, FUR EACH NSET(N-1) XRAT :: = CUUNT R.4TE PFR SECClND DN X FUR Et1CH !'l SET(i'-i-ll MIN~C = YIN~C + NCARO(\FK) MAXrK = M!',XNC + i ~C\RC ( ~ l NOFV = 0 SLY= (ti.78-6.77)/(CY878(NFK)-CY677(NFK)) I F ( ; ~ A X J C 0 0 l GO T J 6 5 00 56 K=MIN N C,M~XNC c l, CH P .,\ S S TH R U TH I S DC L O O P C O VE R S l H E D t\ T A ( G EV t N T S O ~! LfSS) ON CN[ CARC J = S ( Kl) READ (5,40) ( (DETR(I,J+Ll,I=l,3),L=l,8) FURM : d ('3(3F3.0,1X)) DETR(l, ~ ),C[TR(2,N) 1 SETR(3 1 ~) = CETECTUR INPUT CATA FROM X, Y, l Pl OP OE P. 41 DU 5S LK=l,S 4? JLK = J + LK 43 IF (OETR(l,JLK).EQ. C .O .ANO. DETR(2,JLKl.E0. C.O .A N D. 1 DETR.(3,JLK).EQ. G.O) GO TO 56 4 4 C A L L A L. P ~'. A [ ( C Y :n S ( ;\j F K ) f j E Tf~ ( 2 J L K ) S L Y ~ : r-; A L P l 45 IF ( EN ALP .LT. a.a) GC TU 55 46 NOEJ = ~O[V + l 47 48 49 50 .. :,JJ. 52 55 56 57 65 NCIEV cou : ns UP THE GCOD EVENTS l,-j E::\CH S[T LF DATA NOEVTL = ~GEVTO + 1 NU~ : vrc cuur ns UP THC: GOUD cVE::HS FOR. ALL Hfr 01-\TJ\ AT EN[RGY(l,2,NOEVTO) = E~~L? E ; "i:RGY(2,2, t lC:cVTUl = ~'.LU.P DETR(l,~02VTD) = DETS(!,JLKl D E T i1. ( 2 hJ V T D ) = 0 [: H' ( 2 J L K ) Df::TR(!,t ;O VTO} = OET'd1,JLI<) co:n 1 i \UE CC > H ,,U L \ [ 'I !: J r ( ,i l = 'J C F: V NEVt -lf(f~) = 1 l0. : ;crJD c:'/ _~ \ ns l : 'J ~ JS':TUJ-1) CtHT I \!Jc

PAGE 142

133 C t.T THIS rrnt, HAVE k i\C IN ALL Dt1L\ FOK ,\:,jGLt: l l=l,2'30 THIS GC LC P CLE AH S AND Z FlSSIO N FRAGMENT MASS DISTRIGUflU~ ARR\YS TU ZERO X D S f K { L ) = ) MZlJST;~{L) J ivl,~OSTC(L) = 0 hZDSTC(L) = "J M lr'Hf = l TOICT:'-i = : J. ( J TtJTCrC = ;.C' T If.' E = :j ~ TJfXCT = ).:) SU ( 1 c < = ) C, SU 1 -', t Y SLJt 1 cZ = su : ~c r = .-, i"' ._, ...,. .,, .) .J SU 1 ': LXC = ) :: SU LC Y C = C ; J S U ~'. t: Z C = C 0 SU Mt::: TC = :-,.( iJO 26 ) 'J=2, JOEL f A f;\ C H P A S 5 T hi~ U T H I S CC L '] 0 P C C E S Ct1 L C U L A T I Ui S FCJ -:_ A f-..l Erd If~ :: S E T CJ F C A T t l 2 1 i-.i F K = '~ l 1 2 ;: \ E V [ ,'-i T ( l l = n

PAGE 143

C C 123 124 125 126 127 130 131 132 133 134 135 136 137 138 139 rJUE\/A\J = 0 !WEV/,C = 0 M 1\:,i F = 1-1 I 1\} ril: + ; E V H d ( ; F K ) M 1\ X i'~ t = i1 A X f' l F + ;-~ E V U\ T (:'J) lf {MAJ.i'H:: .EQ. 0) GD TO 26C S L X = ( f L E H ) / ( C X L ( i J r K } C X lI ( !\ f K ) ) SLZ = (EL-EH)/(Cll(NFK)-CZH{NFK)) AX = AK/(CXL(NFKl-CXH(~FK)l !. l = AK/ ( CZ L U!F K ) C Zf-l( iff K } ) APX = AKP/(CXL(NFK)-CXH(NFK)) APZ = ~KP/(CZL(NFK)-CZH{~FK)) 3X = BK (AX* CXL(NFK)l Bl = BK (AZ* Cll(NFKJ) 8PX = BKP {APX C~L(NFK)) SPZ = BKP (APZ ClL(NFK)) 134 A,AP,B,BP ARE SCHMITT$ MASS-DEPENDENT ENERGY-CALIBRATION CO t-~ S T t, ~ T S 150 DO 240 J=rINNf,MAXNE 151 MKCT = lJ 152 DU 185 KCT=l,1liKCf 153 IF (KCT .GT. 1) GO TC! 153 C SlRAIGHf LIN~ CALIJRATIO~ IS USED WHEN KCT=l 15 4 t N X ( KC T l =c L ( C XL ( i'l FI< ) DETR. ( 1 J ) ) *SL X l 5 5 :-: il Z ( K CT l = C: L ( C !. L { ;\; F K ) '-:l E TR ( 3 J l ) i:S L l 156 GO TC 16) C MASS DEP~~UENl ~1ERGY C~LiaRATION 158 ENX(KCT) =((~X+ APXTFMASX)(DET~(l,J))) + JX l + (BPX TF~ASX) l 5 9 E: N ( i<. C T l = ( { ,\ Z + A P !. l r: t~ t, S l l -1:( 0 i:: T R ( 3 J l ) ) + b Z l + (BPZ rr~ASZ) C cr~LCUU,T rui OF r ';;\SS C C 160 JIMB ={(TCTALM-ALPHAM)* ~iZ(KCT)-ALPHA~ ENEJGY(l,2,J)) 161 CIMB = E~X(KCT) + ENZ(KCT) 16 2 U rrrn = E \) X ( KC T ) ~\LP r M~ c NE:::?. G Y ( l 2 J ) 165 TF~~SX=((JlK~ CIMJ +2.JDIMD (COSIN*2)l+P~RI.JCCSl \ 1 SCRf(BIMB CI~a CI~3 +(CIM3COSINl*2l l/(CIMBl 166 TFMASZ = TOTALM -4.8C -TFMASX 1 6 7 I F ( K C T t: Q l l _; C T C 1 e 5 168 11 Q 171 172 173 175 176 1 77 18') 1L5 190 KCR = KCT 1 DELTAX = A3S(E~X(KCfl ~~X(~C~l) [ F ( C t:L T .\ X GT J '1 ) ,; rJ T CJ 1 S 0 CELfAZ = ABS(ENZ(KCT) ~NZ(KCR)) IF (DELr~z .GT. 0.5) GC TO l~J [:~J'.:i<.GY(."~:.i,:,.Jl = E~;X(KCT) ~NERGY(~~,3,J) = E\Z{KCTl GO TO l':1) IF (KCT .E(. MKCT) GC TO 175 CU'< f I ; ,u [ SCHMilf U\Lli_,t{t\TIG~J, .~ITH Ct\LCUL:HI0.'-1 UF Mt\SS t\.\J(j ENERGY i.:: : J f i { G Y < i-. ;., 1; J l == c L !: f;,, G Y < N P 1 J l + E ,\ '.: R G Y < N P 2 .J l +

PAGE 144

135 l H1 H~ G Y ( '4 P 3 J ) C C H A;~ G l TH E E 4 [ R G Y V /; Lt._; C S FRO tv rLu A T I f G PO I N T T O I NT E G E R i\ 0 C SU THAT ENE1GY CIST~IEUTIU~ AR~AY5 [AN KE TOTALED UP 191 192 193 194 l ':15 196 197 198 199 C C C 200 201 202 203 C C C 204 2J5 ,~ 06 207 2 08 209 210 212 C C C 215 216 217 218 C C C 219 22() 221 222 ~Z3 224 225 240 C 245 2 1 16 LEX EN:~GY(NP,1,Jl + n.5 LEY= (~.C ENERGY ( N P,2,J)) 15.0 LEZ = ENfRGY(NP,3,J) + J.5 LET= E N ERGY( N P,4,J) + 0.5 XMASS(NP,J) lF M ASX KX = TFM A SX + 0.5 ZMASS( N P,Jl TF MA SL Kl= lFM~Sl + C.5 IF (TFMASX .GT. TFMAS!) GO TO 215 fHl NEXl. 4 STATEM EN TS TOTAL UP THE ENERGY DISTRIBUTIO~ tRR~YS WH[N TH E ANGLE G~TWE EN THE ALPHA PARTICLE A~O lH~ LIGHT FRAGM~NT IS THE EXP~RIME~fAL ANGLE ALPHA KEX(LEX) = KEX(L~X) t l YKE(L f Y,2) = YKE(L f Y,2) + 1.0 KEZ(LEZ) = KEZ(L ~ Zl t 1 KET(Li:T) = V:f:T(Lt :: Tl t l THE ~ f Xr 2 STATEME N lS TGTAL UP THE MASS OIST~IBUTION tRRAYS LHE:N THE l\ ,' ~GLf: .3 F Th r :l~N fHE ~\LPHA PAi-.J f I S T H E c X P c R I 1-' !: > lT 1\ L 1\ \G L E t, L PH A MXUSfk(KX) = MXDSTR(KX) + 1 M Z u S lf\ ( K i'. ) = M ?. L : :. T f{ ( K ?. ) + l su ~~x = SU~EX t EN E~G Y(NP,1,Jl s u // 1 E y = s u jl ~: y + C \ j [ i{ G y { l iJ I 2 J ) SU ~ El SUMfl + ENERGY ( N P,3,J) S U M E T = S U t' Z: T + >:: N E R (; Y LW 4 J l ~VA~ = ~ CEVAN + l GO TL 24:J THE N~XT 4 STATEM b~ TS TOTAL UP THE [ NERGY DIST J I B UTION ARR\YS WH~N THE A~GLE 8ETWE~N THE ALPHA PARTICLE A NC THE LIGHT FR,\GM C l\f IS THE CC~PLI/v'.E1\TARY A,'.GLE ALPHi,C KEXC(L~X) = KEXC(LEX) + l YKEC(LEY,2) = YK~C(L ~ Y, 2 ) + l.J KEZC(L~l) = KEZC{LEll + l KETC(LEfl = KETC(Lf:T) + 1 THE ~~XT 2 STAT EMEN TS TUTAL LP TH~ ~~ss DIST ~ I ~ UTICN ARnAYS WH~~ TH l ANSL ~ BE T ~ ~~N THE A LPH A PARTICLE A ~ O THE LIGHT F i t.:\GMi: : H rs THE cr:r~PLf1 1 t\JTAP.Y ,\t ,JG LE ,UPt-: ~\C MXCSfC(KXl = MXDSTC(KX) t l MZUSTC(Kll = MZOSTC{Kll t l SU MEXC SUMtXC + J, J ~~ GY(.\1P,1,J) SlJ '. lt:YC = SU 1 1E YC + ENf:RGY(NP,2,J) SUMELC = SUMEZC + E~ ~ ~GY(NP,3,J) s u ~ ~Tc = s u ,1 E T c + E j ~ ::G Y ( 1 ~ P, 4 J l l O f:: V ;\ C = 1'-l O :: V 1 \ C: + 1 C Cl .' l I I i'J U ::"= TH E C~LCULATIC~S G ~ C~[ SET CF DAT~ H~VE NCh BE~N COVPLETEU cuu .~n:c ,r-:(J i' JO v:,; \ co1nrc( ~t=Kl = r-10 vAc

PAGE 145

C C C C C C C C C C C C C C C C C 21.,7 24B 249 250 2 51 2 52 253 2 60 261 262 263 2 6't 265 266 136 THE 2 PF<. E V I OU S S f J\ T E M c ~n S G I V E THE NU 0 F E V : N TS I N E /.\CH SET OF DATA AT ANSLE ALPHA AND THE NO. AT ANGLE ALPHAC XCUU~T(NFK} = 36)0.0 XRATE(NFK) Tl~E3D(~FK) STATEVENT 247 GIVES TH~ TOTAL ~O. OF FRAGMENTS DETECTED BY X DURING THE TIME PEKIOD THAT A SET OF DATA IS CCLLECTEU CRATEN(~FK} = COU~TN(NFK)/XCCUNT(NFK) STATE~E~l 248 GIVES TH~ iO. OF EVENTS IN SET NFK(IN WHICH Th E A;~ G L :: B ~= T\1 E E:l T HE AL PH;\ PART I C L E Al' JD THE: L I G HT FRAG~ENf IS THE MEASURED J\NGLE ALPHA) DIVIDED BY TH~ TOTAL FRAGMENTS CETECTcC BY X CRATEC(~FK) = CUUNTC(~FK)/XClUNT(~FK) TOTCTN = TOTCTN + COUNTN(NFK) fOTCTC = TOTCTC + COLNTC(NFK) T a ; E = T I f'/ E: + T U 1 '. E 3 D { i~ F K ) nnxcr = TUTXCT + XCCUH(;ffK) CONT I i W[ THE CALCULAfICNS HAVE ~ow BEEN COMPLETED FOR ALL THE SETS OF DATA Al THIS ANGLE C TRA : ~ = TXC l CT~AC = fUTCTC/TOTXCT THE NEXT 4 STATEMf~TS CALCULATE AVERAGE VALUES FOR THE EVENTS IN WHICH THE LIGHT FR~GMENT IS DETECTED 8Y X i\VGF:.X = SUH:X/TCTCT.~ AVGEY = SU~EY/TOTCfN AVGEZ = SUMEZ/TOTClN AVGET = su~ET/TOfCl~ THE ~EXf 4 ST~TE~ENjS CALCULATE AVE~~GE VALU~S FOR THE t V [ '! T S I N 'f4 H I C. H T H E L I G H T F ,~AG M E ;-H I S O c l E: C T E D 8 Y X A~D THE ANGLE B[T~EEN THE ALP~A PARTICLE ANC THE LIGHT Fi<.AGr-:un IS ;.\LPHAC ( HiS ALPH,4) 267 AVGEXC = SUMEXC/TCTCTC 268 AVGEYC = SUMEYC/fCTCTC 269 AVGEZC SUMEZC/TGTCTC 270 AVG(TC = SUMETC/TOTCTC 2 8 0 WR. I r E ( 6 2 8 1 ) /'. L ? H ;\ !, L PH A M T U T t. L M E: L E H P M{ I 1 :'-JScTS, ;UE:VTC 281 FORMAT (' 1 1 ,' lER lA?.Y AU'H/\-F-ISSIC\ DtdJ\ OLTPUT'//T2, l 'EXPERl~ENTAL ALPH~ ANGLE=',F4.0,T36,'~LPHA M~S5=', 2 F3.l,T54,'M~SS CF FISSIONI~G NUCLEUS=',F4.0/T2, 3 'L I ;; !-~ T F RAG MC r.i T E E ,~ G Y t: L = 1 F 5 l T 3 & h:.: I\ 'IY FR AG~' c fl T 4 T :i l E ~'i ERG Y F: 1-1 = F 5 l T 7 G P ti R I TY= F 3 :) / T 2 5 'NC. SETS OF DAT~=',I2,T3~,'10TAL NUVSE~ CF EVENTS', 6 159, 'FOR THIS EXP~~IMENTAL A~GL~=',I5//) 282 00 29J ~=2,~DELTA 283 NFK = r:-: 2f,4 IF ('ffK .GT. 1.) GC TC 287 .., :.11 'tl:, 286 FORM;\T { 1 ',12,' :FK' ,TJ, 't.LPHA M-.;GLE CGU.;TS' ,T29, l /.\ L ;> h", C l\ "-i SL CCV n S T 5 l \LP H .t CO l.: \TS / X COLN TS f 7 5 2 'ALPHAC COUiTS/t'. CO!JiflS',TlC,3,'X COUi\TS'/)

PAGE 146

137 287 WRIT[ (6,?BB) NFK,COUH\~(f-.;FK) ,COL.:NTC(NFK) ,CFUTEl ~(NFK), 1 CRAfEC(~FK),XCULNT(NFK) 288 FO~MAT (T2,I2,Tl5,F4.CiT37,F4.0,T57,1PE11.3,T82,1PEll.3, 1 Tl01,1PE13.5) 290 corn li'WE 291 Wi<-ITE (6,292) l\LPrt.,P:.kI,HJTCT:\l,CTRA,s; 2 '-J 2 F ORM 1H ( I l I I Mi G L C u ET d C [: ; J AL pH A p AK T I C LC: AN D l.l G H T I T 1+ 1 1 F r~ A. c l'-i ;::; = F :;; 1 r 6 1 P ,\ R r r Y = F 3 o r 1 s 2 1 1\;0. CF E:VE!JTS= 1 ,F5.C/T2, 1 T(JTAL i',;C. CF EVENTS',T22, 3 'LlVIDEU BY T Ttl X CUUNTS=',lP~ll.1) C S TAT E r-, [f~ f S 2 9 3 T H RU 3 .:::: 3 ~l I T t OU T DA Ti\ F U f!. T H E C ,,., S E S 1 N C vJ H i C h T H E ,\ :1 G L t i3 E T ,-1 E E N TH !: AL P HA P AR T I C L E: /\ fW Th[: C LIGHT FRAGK~NT rs THE EXPERIMENTAL ANGL~ ALPHA C ThE FGLL ~ING ST~T[MENT IS TH~ RLADOUT OF MASS DISTRIBUTION C C C C C C C 293 WRIT[ (6,294) (NU(K),MXUSTR(K),NC(K+50) 1 MXOS1R(K+50), 1 NO(K+l00),MXDSTR(K+lJO),NO(K+l50),MXOSTR(K+l58), 2 /\i U ( K + 2 CO ) M X DST? ( i< +? G G ) rw ( K l Ml u ST R { I<. l NC ( K + 5 0 ) 3 MZDSTR(K+50) ,NO(K+lOOl,~ZDSTR(K+lCO),NG(K+l50l, 4 M 7. U S T R. ( K + l 5 ~i ) :W { i( + ? 0 Cl ) M ?. D S Tr<, ( K + 2 CJ () l K = l 5 0 ) 294 FURM.1\T (T1.,'.X MASS lJISH /, :~ I T C TC T > ~ 1 C 1' Rt, i'i 'd ?, IT:.: ( 6, 2 9 7 l t, V ; t X, /i. VG l: Y, A 'I GE Z. AVG [ T F C ;-,, i~ ,\ T ( T 2 1\ VG X E: \! ;{ G Y = F 5 l T 2 6 A V :; f, LP HA PA R l I C L !::: T 1 t6, 1 f.r L=RGY=',F5.1,T62, 'AVG. l ENERGY=' ,F3.1,T86, 'AV:~. TUTt,l Ei;E~r.,;Y=' ,F'.:>. 11) R~AOCUT OF X,Y,l ENE~GY OISTRIBUTIO~~ 2 9 8 ~-; P. l f '= ( 6 2 9 (J ) ( N U ( K ) K ::: X ( K l t,1 C ( K + 5 C ) K E X ( K + 5 j ) :,1 0 ( K + l C 1 ) ) 1 KE I. ( K + i :) :; l YI<. [ ( l< l ) Yi< c ( K 2 ) ''-J CJ ( K ) K '.: Z ( K ) NU ( K + 5 C ) 2 KE l ( K + '5) ) 1 LJ ( K + 1 C :1 ) 1 n: Z ( K + l CO) K = 1 5 0 ) 299 FOR~AT (T~,x E~:RGY DISTRIBLTl0\ 1 ,T42, 1 ALPhA PARTICLE', 1 r 5 7 E ~i ::: R G v L r s r r 2 o z E N R. G Y o r s r ? 1 B u r r c N 1 1 T 2 2 3(' c ',1X,'GISf~',3Xl,T54,':',T59,'CISTR',Te3,_ 3 3( 1 f ',lX, 'DJST~,3~)/(I3,2X,I3,4X,I3,21,I3,4X,I3,2X, 4 .. :) I3,T5j,F4.l,T~8,F~.l,TB2,13,2X,!3,4X,I3,21,l3,4X,l3, 2X,I3,4X)) :"{L\OOL;T ;JF PRE:Ll:HJ/~:::y U,FlirU 1 1 \TIC1\ GlSTHl0UTICJ I B~FCR~ TCl~L ENERGY 3 0 0 ti R I L: ( 6 2 g 2 ) f1 L P f-1 f P !\ R I T C T C T N C T rU\ i'J REAOGUT SF TOTAL ENERGY CISlRlGUlIC~ J O 2 w R I l L ~ ( 6 3 C; J ) ( iJ ( j ( K ) K E T ( K ) N fj ( Kt 5 Ci ) K E T ( K + 5 ; ) N (J ( K + l C O ) 1 K E l ( iH 1 :-i :) ) l O ( K + 1 ':i ) ) K E T ( K + 1 5 0 ) :J(J ( K + 2 C J ) K :: T ( !< + 2 0 0 ) 2 t;(j ( K + 2 5'J ) 1 K T ( K-+ 2 '3 J l I<,= 1) 5 C ) 3 :; 3 F u R M .t. r c o r 2 r c T/1 L i:: i R G v c r s r R r B c r ICJ \ J 1 1 l 6( 1 i: ',lX,'CISn',4X)/6(13,lX,D,6X)) S T.[. T C:: 1'' F ;,;r S 3 ) 1 TH ::t lJ 3 16 L iH 1 ::: CJ LU O !-, L\ F G F. T 1-: :::: C ts. S C: S U 1--1HICt" TIE A -iGLc: Bff)Ef\J THE /'.,LPh;'; P/\:<.TICLc Ar,D Tl-;t:

PAGE 147

138 C L I (;f-H F ?./1 CME N T I s r H E CO Mp L r ME N T A p y /d~ G L E A L pH A C 3 Ci 4 'rJR I T [ ( 6 2 'Jt ) /\ L P HA C P 1\ R I T CJ T C T C C TfU1 C C R [/,Du lJ r en= r< ,\ s s [) l s T :( l [) u T I C ,~ 3 (J 5 iIR I T t: I G 2 9 1 t) ( NU ( K ) t .' X D S TC ( K l 1 ,W ( K + 5 0 ) H X D S T C ( K + 5 0 ) 1 N (K+l0J),MXOST~(K+100l,NO(K+l50),MXDSTC(K+l50), 2 NO(K+208l,MXDSTC(K+2JG),N (K),MZUSTC(K),NC(K+50), 3 fJZDSTC{K+5D) ,rJO(K+lOC),~.'ZOSTC(K+lO'Jl ,NC(K+l50), 4 MZDSTC(K+l5Jl,N (K+2CO),MZOSTC(Kt20J), K=l,50) C READOUT UF PRELI1"1PU\1Y I'ffURMATIUi\ BEFORE: ENERGY DISTR. 31/J WRITc (6,292) ALPH;,\C, PMU, rurcrc, CTR,\C 311 (6,297) ,'\V;;cxc, ,ft...VGEYC, r .. VGi::ZC, .l,VGETC C RF MHi UT U F X, Y, Z EN b{ G Y DI SH( I3 UT I (),'JS 3 1 2 R I T f.: ( 6 9 9 ) nm ( K ) lC X C ( K l I N O ( K + S O l K E X C ( K + 5 0 ) N C ( K + 1 0 C j ) 1 Kc X C ( Ki l O O) Y !< = C ( K l ) Y l: EC ( I< 2 ) :\JO ( K ) KL: Z C ( K ) 2 ND(K+50),KEZC(K+5J),NU(K+l00),KEZC(K+l00l, K=l,SC) C READUUT CF PRELIMINARY I~FORVATIUN BEFORE TUTAL ENERGY C CISTRI8UTIO~ 315 \~RIT[ (6,?.'"..J2) ALPHAC, Pi'\;~f1 TOTCTC, CTRI\C C READUUf OF TOTAL ~NEPGY OISTRI3UTION 3 16 i'i R I T E ( 6 3 0 3 l ( N t:1 ( l( l !< f: TC ( K ) NO ( K + Cl ) KE 1 C ( I<+ 5 ~ : ) ~-JO ( I<. + 1 0 J } 1 K !:= T C ( K + l 'J O l :\J O ( t". + l 'j ., ) K [ T C ( I< + 1 5 0 l N U I K + 2 0 Q ) 2 n.T ,~ ( K -1 ?. C ') l ~w ( K + 2 'j 0 ) K E T C ( t<. + 2 ~j ") l K = l 5 0 ) ,,oa co;n Ii\UE C: Sl1\T-f.'E.1\lS 32:l THRU 333 f{f:M)UUT TH: D,\T!, EV:'H BY EV':i\T 320 WRITl (G,321) ALPHA, 1IME, NSETS, ~OCVTO 3 2 1 t= [F( M A r c 1 PR Pi HJ u r o F II L P H r, F r s s I CJ : .. J o !H /\ F c R E Ac H r 4 2 l 'EVdH 1 //T2, ~XP'.:RIMENT,'\L ,\LPH1\ Ai\::;LE:=' ,F,i.0 1 2X, 2 'fUTLL TI~E CN 3 =',F5.2,2X,'NO. SETS OF OATA= 1 ,l2,2X, 3 TO L\ L ; ~ 0 0 F l V ;:: >H S A T TH I !:. :: :< P A. u_; L E = ; I 4 / /} 3 2 ? M I ,\ ; ~ f = 1 3 2 3 M A X .' i.:. = ~. 3?. 4 DU 3 1 t ,: ;\ = 2, rHJ EL T .t1 3 2 5 -~ rI< = J-l 3 2 6 i"1 I ~\ \ :_= r; I f'\ ~l E + 'J EV Et; T ( fi F K ) 3 2 7 MAX ;J [ = ,'' : X rJ ~'. + N E \/ E ; H ( N l 3 3 J 1~ R I ft: ( 6 3 3 1 ) ( ,'l F K ) C XL ( ;~ := K ) ( '; F K ) C X H ( :\if K ) ( NF K ) l CY 2 7 3 ( "l F K ) ( NF K ) C Y 1 ) 7 7 ( i-; F i'. ) ( \ F K ) C !. L ( F K ) ( .. F K ) 2 CZH(\lFK) J31 FOR:1:,T (' CXL( ',12,' )=',f4.0,4X,' CXH( 1 ,I2,' )::',F 1 ,.0, l 4X,' CYf\"78( ',12,' l=',F4.l,,,X,' CY6-f7( ',12, 1 )=', 2 F 4 l 4 X C l L ( I I 2 ) = I F 1 1 ,') 4 X 3 C Z t" ( I 2 1 l = f ENE ,{ G Y < 2 1 J l 3 E \j E .~ G y ( 2 I 3 J ) t E ,_ t R G y ( 2 ft J ) t /, /f. 1\ s s ( 2 j ) t 4 ZMASS(2,Jl, J=rI~~E,PAX~E) 3 3 3 Fu R ri f_,, 1 < Ev t 1\ r r 3 :~ '= 1 x 1 r 1 3 :.,, F T v T 1 i L ::: T z r 2 4 1 i\ l ;> L >l T 3 1 1 ~J ~:. :{ T ':5 2 1 ; E '1 l TL+ 5 TUT/\ L N E 1 1 2 T s o M I, s s x 'l T 6 6 ,-.1 :\ s s z "J T 7 6 P ;::, i x T ,3 ,, P f. ~ J l 3 l -.1 G l O T A L fJ E '.j T l C 3 1 ~'. ; \ S S X O T 1 l 1 / : ,\ S S Z P 1 / ( T 3

PAGE 148

139 4 I 3 ,. T 8 F 1 t Q T 1 3 F L1 Ci T l G I F 4 0 T 2 ::i F 5 1 T 3 2 F 5 1 T 3 9 5 F 5 l T ii h F 5 l T 5 9 F 5 1 T 6 7 F 5 l r7 7 F 5 1 18 Li F 5 1 6 TQ3,F5.1,r1n4,F5.1,Tll2,F5.l)) J40 CONTii\Uc 1 tl0 COtHlf':UE: END SU 3 R (JUT I ;,J : ,\ L H;\ E ( CY CE SLY CJ/.\ LP ) C Pi~OGR/\M CALCUL/\T[S [::,;:::Rr_;y CJF ALPh/\ PARTICLE C0MMCN UELTAE(2bJ) S G 1 E 1'-l f, L P P = D 7. 8 ( C Y 0 E ) S LY 502 KEAL10 = (ENALPP + 0.05) 1c.o 503 EALlO = KEAllO ~04 ENALPP = EALlO/lJ.0 C fN,I\LPP IS ;n:i~: HJ TERYS Gf' TEIHH'S CF ,vEv C [:\Jf,LPP 1S TH:: ALPH,~ ~NE::tGY AFTER PASSING THRUV;H THE C NICKEL FCIL 505 I = (10.1 lNALPPl 39.C ~06 ENALP = :NALPP + DELTA~(l) C RUUNL: UfF ALPH, t 1 ffR~Y TD r;C::,'\REST 0.5 MEV ~07 KEAL2 = (E\tLP 2.0) + 0i5 5GB EAL2 = KEAL2 509 lNALP CAL2/2.0 Kl:TU~~:\ EN[:

PAGE 149

APPENDIX D DERIV ATION FOR ANGULAR DISTRIBUTION CALCULATIO NS

PAGE 150

Consider detector Y (for alpha particles ) at an experimental ang~e e with respect to fission fragment de tector X via the U 235 source at points. If Y is held at angle e and revolved around the axis between X and S, it sweeps out a zone on the surface of a sphere. The area (A) of this zone is, (Dl) A= G W 2 Where, w = w i dth of square detector y G = geometry factor G = nWsin0 2(L 2 2 l r a..., ,... 4.., .-( 1, T I') T ) l 2 I W )2 T L J. ...... VU..! J "/ (... .a..J J (D2) G (2 nL / W ) sine Where, L = di stance from center of detector(Y) to source ( S ) e = angle betvreen the detector (Y) source ( S ) and the sym m etry axj_s (d etector X). then, A [(2nL/W) sine ] W 2 141

PAGE 151

(D3) A= 2 nWL sine The solj_d angle which this zone subtends is, Solid Angle== 21rWL sin0 12 (D4) Solid Angle= (2nW sin0)/L let, 1~2 Total nu mber of LRA events detected at 0 z = '1 1 otal nu mber of fission fra gment s detected by X Multiplication of this factor by G gives the number of LRA particles emitted at an g le e j nto the zone swept out by Y when revolved around the axis, divided by th e total number of fission fragm en ts detected by X. This is the LRA fission rate ate compared to the binary fission rate. R = = Z G Division of this by the solid angle subtended by the zone gives the LRA fission rate ate compared to the binary rate, all per unit solid angle. Z G R/sr = Solid Angl Multiplication of this by a normalization factor (F) will give the relative number of counts compared to the number at a reference angle. For this experim en t, the refer ence a~gle was e = 85 and the nu mbe r of counts at this angle was adju ste d to be 1000.

PAGE 152

Therefor e th e relative numb er of cou nts (R.C.) at any angle is calcul ated by, This gives (D5) = Z (2 nL / W ) sine (2 TTW / L ) s:tne R.C. = ZFL 2 w2 F

PAGE 153

BIBLIOGRAPHY 1. R. D. Present, Phys. Rev., 59, 466(1941). 2. L. W. Alvarez, quoted by Farwell, Segre, and Wiegand, Phys. Rev., 7_!, 327(1947). 3. N. A. Perfilov, Yu. F. Romanov, and Z. I. Solov'eva, Soviet Phys.-Uspekhi, l, 542(1961). 4. E. K. Hyde, The Nuclear Properties of the Heavy Elements III, Fission Phenomena, En g le w ood Cliffs, New Jersey: Prentice-Hall, 1964. 5. T. Methasiri, Atomic Energy Establishment Trombay, Bombay, Report No. AEET-235 (1965). 6. J. E. Gindler and J. R. Huizen g a, Nuclear Chemistry II, New York, New York: Academic Pre 8 slnc. ~affe, ed.), 1968. 7. Tsien San-Tsian g Ho Zah-Wei, R. Chastel, and L. Vigneron, ~phys. radium,~' 165 and 200(1947). 8. E. 0. Wollan, C. D. Moak, and R. B. Sawyer, Phys. Rev., 72, 447(1947), 9. G. Farwell, E. Segre, and C. Wiegand, Phys. Rev., 71, 327(1947). 10. K. W. Allen and J. T. Dewan, Phys. Rev., 80, 181(1950). 11. C. B. Fulmer and B. L. Cohen, Phys. Rev., 108 370(1957). 12. M. Sowinski, J. Chwaszczewska, M. Dakowski, T. Kroguliki, E. Piasecki, and W. Przyborski, Institute of Nuclear Research, Warsaw, Report INR No. 765/IA/PL (1966). 13. S. L. Whetstone, Jr. and T. D. Thomas, Phys. Rev., 1 5 11 11 7 4 ( 19 6 7 ) 14. R. A. Nobles, Ph y s. Rev., !_26, 1508(1962). 144

PAGE 154

15. E.W. Titt e rton, Natu r e, 1.68, 590(1951). 16. L. L. Gr e en and D. L. Lives e y, N a tu r e, !_59, 332(1947). 17. L. Mar s h a ll, Phys. Rev., 75, 1339 ( 1949). 18. I. G. Schrod er Ph.D. Th e sis, Colu m bia University (1965). 19. E.W. rritte r ton, Phys. Rev., 83, 673(1951). 20. N. A. Perfilov and Z. I. Solov'ev a Soviet Atomic Energy; 2, 175(1958). 21. V. A. Hattan ga di, T. Meth a siri, D. M. Nadkarni, R. Ramann a and P. N. R a ma Rao, Sy mp osium on the Physics and Ch e mistry of Fission (International Atomic Energy Agency, Vienna, 1965), Vol. II, p. 397. 22. W. D. Loveland, A. W. Fairhall, and I. Halp e rn, Phys. Rev., 16]., 1315(1967). 23. N. A. Perfilov, Z. I. Solov'ev a and R. A. Filov, Soviet Phys. JE rP, 1.2, 1515 ( 1964). 24. Z. Fra e nkel and S. G. Thompson, Phy s Rev. Letters, 1J., 4 3 8 ( 19 6 1 -1) 25. Z. Fra e nkel, Phy_~ Rev., 156, 1283(1967). 26. J. C. Watson, Phys. Rev., l?l, 230(1961). 27. N. A. Perfilov, Z. I. Solov'eva, and R. A. Filov, Soviet Phys. JETP, ~, 7(1962). 28. N. A. rerfilov, Z. I. Solov'eva, R. A. Filov, and G. I. Khlebnikov, Soviet Ph y s. JETP, D_, 1232 ( 1963). 29. N. A. Perfilov and Z. I. Solov'eva, Soviet Phys. JETP, 10, 82l~(l960). 30. V. N. Dmitriev, L. V. Drapchinsk i i, K. A. Petrzhak, Yu. F. Romanov, oviet Physics-Doklad ~ i, 823(1960). 31. Z. I. Solov' eva and R. A. Filov, Soviet Ph y ~ }E'l '. 16, 809(1963). 32. V. N. Dmitriev, K. A. Petrzhak, and Yu. F. Rom a nov, Soviet Ato m ic En~ ~ g ;y.:_, 15, 659(1964). 33. H. W. Sch m itt, J. H. Neiler, F. J. Walter, and A. Ch e t!-1a m -S t ro de Ph y s. R e v. L e t t ers, 2 4 27 ( 1962)

PAGE 155

34. I. Halpern, Symnosium on the Physics and Chemistry of Fission (International Atomic Energy Agency, Vienna, 1965), Vol. II, p. 369. 35. R. Ramanna, K. G. Nair, and S. S. Kapoor, Phys. Rev., 129, 1350(1963). 36. I. Halpern, CERN Report No. CERN-6812, 1963 (unpublished). 37. S. L. Whetstone, Jr. Phys. Rev., 114, 581(1959). 38. N. Feather, Proc. Roy. Soc. Edin., 66A, 192(1964). 39. N. Feather, Symposium on the Physics and Chemistry of Fission (International Atomic Energy Agency, Vienna, 1965), Vol. II, p. 387. 40. N. Feather, Nature, 159, 607(1947). 41. V. F. Apalin, Yu. P. Dobrynin, V. P. Zakharova, I.E. Kutikov, and L.A. Mikaelyan, J. Nucl. Energy, 13A, 86(1960). 42. E. Nardi and Z. Fraenkel, Phys. Rev. Letters, 20, 1248(1968). 43. J.C. D. Milton and J. S. Fraser, C a n. J. Phys., 40, 1626(1962). 44. J. S. Fraser, J.C. D. Milton, H. R. Bowman, and S. G. Thompson, Can. J. Phys.,:!]_, 2080(1963). 45. C. Williamson and J. P. Boujot, "Tables of Range and Rate of Energy Loss of Charged Particles of Energy 0.5 to 150 MeV", Ra p pt. CEA 2189 (Centre Etudes Nucl. Saclay, France, 1962). 46. H. W. Schmitt, W. M. Gibson, J. H. Neiler, F. J. Walter, and T. D. Thomas, Symposium on Physics and Chemistry of Fission (International Atomic Energy Agency, Vienna, 1965), Vol. I, p. 531. 47. M. L. Muga, H. R. Bowman, and S~ G. Thompson, Phys. Rev., 121, 270(1961). 48. G. M. Raisbeck and T. D. Tho n1 2.s, Phys. Rev.,.!]_~, 1272(1968). 49. Y. Boneh, Z. Fraenkel, and I. Nebenzahl, Phys. Re2., 156, 1305(1967).

PAGE 156

BIOGRAPHICAL SKETCH Glen Roberts Bethune, born June 18, 1940, at Abbeville, Alabama, was graduated from Abbeville High School in 1958. In August, 1962, he received the degree of Bachelor of Science in Chemistry from the University of Alabama, Tuscaloosa, Alabama. In September, 1962, he began graduate work in chemistry at the University of Florida, Gainesville, Florida. In December, 1964, he received the degree of Master of Science with major in chemistry. He then continued graduate work at the University of Florida. He has held graduate teaching and research assistantships from the Department of Chemistry and a rescarch assi stantship from the Division of Nuclear sciences. Glen Roberts Bethune is married to the former Sherry Y. Gano and they are the parents of one child. )_4 ~(

PAGE 157

This di ssertati on was pr epared und er the direction of the ch airman of th e candid a te's superviso ry co mmi ttee and has been approved by all members of that co mm itt ee It was submitted to the Dean of th e Coll ege of Arts and Scienc es and to th e Gradu a te Council, and w as approved as partial fulfillment of the requirem en t s for the De gree of Doctor of Philosophy. Au g ust, 1969 Dean, Gr a du a t e Sup er visor y Co m m ittee: